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Syllabus

The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).Find the ratio of their mth term.

^{2 }: n^{2.}show that the ratio of the m^{th}and n^{th}terms is (2m-1) : (2n-1)^{2}/2 + 5n/2, find its 25^{th }term.Answer given:1050+1260-300=2010

Please explain with working.

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7 : 15. Find the numbers.the sum of the two numbers is 25 and the reciprocals is 3/10. find the numbers

If the m

^{th}term of an A.P. be 1/n and n^{th}term be 1/m, then show that its (mn)^{th}term is 1.the nth term of an AP is given by a

_{n}= 4n - 5,then find the sum of first 25 terms of the AP.IF THE SUM OF FIRST m TERMS OF AN AP IS n. AND THE SUM OF FIRST n TERMS IS m, THEN SHOW THAT THE SUM OF ITS FIRST( m+n) TERMS IS -(m+n).

Maths Project :make designs using arithmetic progression

if the pth term of an A.P is q and the qth term is p, prove that its nth term is (p+q-n)

the sum of the first n terms of an AP is given by s

_{n}=3n^{2}-n , determine the AP and its 25^{th}term.a)Find the expression for number of plants in the nth row.

i) 2n + 1

ii) 2n − 1

iii) 4n − 1

iv) 2n + 3

b) Find the number of plants in the 7th row.

i) 21

ii) 7

iii) 15

iv) 17

c) If there are 25 plants in the last row, find the total number of rows.

i) 11

ii) 10

iii) 13

iv) 12

d) Assuming that Reema has kept distance between any two consecutive plants

in a row as 30 cm, find the length of the 12th row (i.e. the distance between

the first and the last plant in the 12th row neglecting the width of the plants).

i) 7.5 metres

ii) 7.2 metres

iii) 6.9 metres

iv) 7.0 metres

e) Reema’s father gifts her 50 more plants. She continues to arrange these

plants in Arithmetic Progression. She observes that she is falling short of

some plants to complete the A.P. How many minimum number of plants

does she require more to complete the A.P. ? (Assuming 25 plants in the last

row before her father gifts her 50 plants).

i) 6

ii) 7

iii) 8

iv) 5

If m times the mth term of an A.P is equal to n times its nth term, show that the (m+n)th term of the A.P is zero.

Find the middle term (s) in the A.P. 20,16,12,.........-176.

the sum of first six terms of an ap is 42 .the ratio of its 10th term is and its 30th term is 1:3. calculate the first and thirteenth term

A sum of ₹1408 is used to give 16 cash prizes to cricket players of a school for their overall test performance. If each prize is ₹10 less than it's preceding prize find the value of each of the prizes.

The sum of the third and seventh term of an A.P. is 6 and their product is 8. Find the sum of the first sixteen terms of the A.P. .

if 3x+k,2x+9 and x+13 are three consecutive terms of an AP.,Find k.If pth , qth and rth term of an AP are a,b,c respectively , then show that

(a-b)r +(b-c)p + (c-a)q = 0

Please help me with this question asap .

if 1+2+3+..............+n = 666, find the value of n.

150 workers were engaged to finish a piece of work in a certain no. of days. 4 workers droped d 2nd day, 4 more workers droped the 3rd day n so on..... it takes 8 more days to finish the work now ..find d no. of days in vch the work waz completed....

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the

If the sum of first 7 terms of an AP is 49 and that of first 17 terms is 289.Find the sum of first n terms

Q) The sum of the first five terms of an AP is 25 and the sum of its next five terms is -75.Find the 10th term of the AP?

Q)In an AP the first term is 8 and the common difference is 7.If the last term of the AP is 218,find its middle term?

The sum of n terms of two ap are in ratio (5n+4) : (9n+6) Find the ratio of their 18th term?

plzz reply with solution

Which term of the sequence 7.3, 6.9, 6.5, 6.1, .... is the first negative term?

Q.Find the common difference of an A.P in which ${a}_{16}-{a}_{12}=16$the ratio of the sum of n terms of two AP's is (7n+1):(4n+27).find the ratio of their m th terms.

Answer: let a1 , a2 be the 1st terms and d1 , d2 the common differences of the two given A.P's. then the sums of their n terms are given by

Sn = n/2 {2.a1+(n-1)d1} and Sn' = n/2{2. a2 +(n-1)d2}

Sn/Sn' = n/2{2.a1+(n-1)d1} / n/2{2.a2 + (n-1)d2}

Sn / Sn' = 2.a1+(n-1)d1 / 2.a2 + (n-1)d2

it is given that

Sn / Sn' = 7n+1 / 4n + 27

2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7n+1 / 4n+27 ........................ (i)

To find the ratio of the mth terms of the two given AP's , we replace n by (2m-1) in equation (i)

therefore, 2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7(2m-1) + 1 / 4(2m-1) + 27

a1 + (m-1)d1 / a2 + (m-1)d2 = 14m - 6 / 8m + 23

Hence, the ratio of the mth terms of the two A.P's is (14m - 6) : (8m + 23)

My question is, why it has been assumed (2m-1) in the place of 'n' ? has it been arrived from solving with the help of a formula or is it a mere assumption? if it is simply an assumption, why it should be assumed as (2m-1) ? why not 2m or (m - 1)

t

_{n}= n^{2}, where n is even andt

_{n}= n^{2}- 1 , where n is oddIf s

_{n}, the sum of first n terms of an AP is given by s_{n}= (3n^{2}-4n), then find its nth term.Find the middle term of A.P. 1,8,15,...........505.

Solve with all steps

If the sum of m terms of an A.P is the same as the sum of n terms of the same A.P, show that the sum of its (m+n) terms is zero.

how many terms of an AP must be taken for their sum to be equal to 120 if its third term is 9 and the difference between the seventh and second term is 20

what are the uses of arithmetic progressions in daily life? i want atmost 10, pls help me as soon as possible

find the 4th term from the last term of the A.P 4, 9, 14,............ 254.

if the nth term of an AP is (2n+1) find the sum of first n terms of the AP

sum of first p , q and r terms of an A.P. are a , b and c respectively. Prove that :

a/p (q-r) + b/p(r-p) + c/r (p-q) = 0

If S

_{1}, S_{2}, S_{3}are the sum of n terms of three AP's the first term of each being unity and respective common diffrence being 1 , 2 , 3_ _ _ _ _. Prove that S_{1}+S_{3}= 2S2.whch one of the following is not an AP:

(A)13,8,3,-2,-7,-12

(B) 10.8,11.2,11.6,12,12.4

(C) 81/7,18 2/7,28 3/7,48 4/7,58 5/7

(D) 8 3/23,11 6/23,14 9/23,17 12/23

which term of an AP 3,15,27,39............ will 132 more than its 54

^{th}termDivide 56 into 4 parts which are in AP such that hte ratio of product of extremes to the product of mean is 5 : 6? Hoping for a quick response......plz.....[ May be within Sunday ]

if sum of n terms of an AP 2n

^{2}+ 5n, then find its n^{th}term.In an AP,the sum of first n term is 3n2/2+13n/2

find its 25th term

find the middle most term of A. P 7 ,10 , 13 ,...........151

solve the solution 1+4+7+10.............+x = 287

if Sn denotes the sum of first n terms of an A.P., prove that S12=3(S8-S4).

A student taking test consisting of 10 quetions is told that each after the first is worth 2 mks more than the preceding ques. If 3rd ques. of the test is worh 5 mks..,what is the maximum score that the student can obtain by attempting 8 questions.

the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. find the first 3 terms of the AP.

how many terms of AP : 20, 58/3 , 56/3 should be taken so that their sum is 300. explain the doublet answer

Divide 32 into 4 parts which are in A.P. such that the product of extremes is to the product of means is 7:15.

In an AP if the sum of 4th and 8th terms is 70 and its 15th term is 80 then find the sum of its first 25 terms some one

answer fast plzzzzzz its urgent

30) the digits of a positive integer,having three digits are in A.P. and their sum is 15.the number obtained by reversing the digits is 594 less than the original number.find the number.

how many multiples of 4 lie between 100 and 250.also find its sum

Find the sum of all the integers between 100 and 200 that are not divisible by 9

In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.^{th}metre and a;so total cost of boring a well of 60 metre deep.A

contractoremployed150 labourersto finish a peice of work in a certain no. of days.4 workerswent away thesecond day,4 more workerswent away thethird dayandso on. Ifit took 8 more daysto finish the work ,find the no. of days in which the work was completed.

ANURAG.The sum of n 2n 3n terms of an AP are S1 S2 S3 respectively. Prove that S3=3(S2-S1).

FIND the 4th term from the end of the A.P. ................ 2 , 5 , 8 ................ , 35Find the sum of first five multiples of 3?

(i) She can pay a lumpsum amount of Rs 2200000.

(ii) She can pay Rs 400000 cash and balance in 18 annual instalments of Rs 100000 plus 10% interest on the unpaid amount.

She prefers the option (i) and donates 50% of the difference of the costs in the above two options to national Relief Fund.

(a) What amount was donated to National Relief Fund?

(b) By choosing to pay a lumpsum amount and donating 50% of the difference to national Relief Fund. Which value is depicted by Mamta?

Which term of AP:121,117,113,......., is its first negative term?

Which term of the sequence 17, 16

^{1}/_{5}, 15^{2}/_{5}, 14^{3}/_{5}, ........... is the first negative term?find the sum of all the natural numbers between 200 and 300 which are divisible by 4.

help plsss

how to multiply 15=a+2d by 25= 2a+9d please anwer just now as my test is tomoorow

The angles of a quadrilateral are in a.p. whose common difference is 10degree.Find the angles.

how many terms of the AP 72,69,66,..make the sum 897 ?

If there are (2n+1) terms in A.P,then prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n.

Find the 20th term from the last term of the AP 3, 8, 13, .....253.

Q1 Which term of the AP 3,14,25,36....will be 99 more than its 25th term.Q2 the first the last terms of an AP are 8 350 respectively if its common difference is 9 how many terms are there what is their sum.

If s

_{n }denotes the sum of n terms of AP whose common difference is d and first term is a, find s_{n}-2s_{n-1}+s_{n-2}3 times the 10th term is equal to 5 times the 20th term. Find the 20th term.?

Show that sum of an AP whose first term is a,the second term b and the last term c,is equal to (a+c)(b+c-2a)/2(b-a)..Plzzz i need hlpp!!!!

1. What is minimum number of days he need to practice till his goal is accomplished?

2. Write the AP for the above situation.

if the Pth term of an AP is Q and its Qth term is P then show that its (P+Q)th term is zero/

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

31. For what value of m are the m

^{th}terms of the following two A.P.s the same?(i) 1, 3, 5, 7,....

(ii) 4, 8, 12, 16,...

in an AP,the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP.

If S

_{n }=(3n^{2}+2n) , find the first term and the common difference of the AP.if sn denotes the sum of first n trems of an ap, prove that s12=3(s8-s4)

find the sum of all the multiples of 7 lying between 500 and 800.

THE ANGLES OF A TRIANGLE ARE IN A.P.THE GREATEST ANGLE IS TWICE THE LEAST.FIND ALL THE ANGLES OF THE TRIANGLE.

Third term of an A.P is 17 and the 10

^{th}term is 50 less than the 20^{th}term. Form the A.P