NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series — Exercise 9.20

Question 1:Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.

Question 2:If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

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Question 3:Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3(S2 – S1)

Question 4:Find the sum of all numbers between 200 and 400 which are divisible by 7.

Question 5:Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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Question 6:Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

Question 7:If f is a function satisfying f (x +y) = f(x) f(y) for all x, y Î N such that f(1) = 3 and 1 ( ) 120 n x f x = å = , find the value of n.

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Question 8:The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

Question 9:The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

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Question 10:The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

Question 11:A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

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Question 12:The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

Question 13:If a bx a bx b cx b cx c dx c dx x + − = + − = + − ( ¹ 0) , then show that a, b, c and d are in G.P.

Question 14:Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn.

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Question 15:The pth, qth and rth terms of an A.P. are a, b, c, respectively. Show that (q – r )a + (r – π )b + (p – q )c = 0

Question 16:If 1 1 1 1 1 1 a ,b ,c b c c a a b æ + ö æ + ö æ + ö ç ÷ ç ÷ ç ÷ è ø è ø è ø are in A.P., prove that a, b, c are in A.P.

Question 17:If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P.

Question 18:If a and b are the roots of x2 – 3x + π = 0 and c, d are roots of x2 – 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q – p) = 17:15.

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Question 19:The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that ( 2 2 ) ( 2 2 ) a :b = m + m – n : m – m – n .

Question 20:If a, b, c are in A.P.; b, c, d are in G.P. and 1 1 1 , , c d e are in A.P. prove that a, c, e are in G.P.

Question 21:Find the sum of the following series up to n terms: (i) 5 + 55 +555 + … (ii) .6 +. 66 +. 666+…

1. Show that the sum of (m + n)th and (m n)th ter

Question 22:Find the 20th term of the series 2 × 4 + 4 × 6 + 6 × 8 + ... + n terms.

Question 23:Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +…

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Question 24:If S1, S2, S3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that 9 2 2 S = S3 (1 + 8S1).

Question 25:Find the sum of the following series up to n terms: 3 3 3 3 3 3 1 1 2 1 2 3 1 1 3 1 3 5 ... + + + + + + + + +

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Question 26:Show that 2 2 2 2 2 2 1 2 2 3 ( 1) 3 5 1 2 2 3 ( 1) 3 1 ... n n n ... n n n × + × + + × + + = × + × + + × + + .

Question 27:A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

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Question 28:Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

Question 29:A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.

Question 30:A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

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Question 31:A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

Question 32:150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.