KC Sinha Mathematics Solution Class 11 Chapter 17 Sequences and Series : AP Exercise 17.5

Exercise 17.5

Page no 17.32

Question 1

Find the single arithmetic mean between :

(i) 7 and 31 ;

(ii)

$(a-b)$ and

$(a+b)$ ;

(iii) 6 and

$-18$ .

Question 2

Insert 6 numbers between 3 and 24 such that the resulting sequence is an A.P.

Question 3

Insert 7 A.M.'s between 2 and 34 .

Question 4

Insert 5 numbers between 8 and 26 such that the resulting sequence is an A.P.

Question 5

Insert 4 A.M.'s between 4 and

$19 .$

Question 6

$A_{1}, A_{2}, A_{3}, A_{4}$ and

$A_{5}$ are the five A.M.'s between 2 and 8 , then find the value of

$A_{1}+A_{2}+A_{3}+A_{4}+A_{5}$ .

Question 7

$n$ arithmetic means are inserted between 20 and 80 such that the ratio of first mean to the last mean is

$1: 3$ , find the value of

$n$ .

Question 8

$\frac{x^{p}+y^{p}}{x^{p-1}+y^{p-1}}$ be the A.M. between

$x$ and

$y$ , then find the value of

$p$ .

Question 9

If the A.M. between

$p$ th and

$q$ th terms of an A.P. be equal to the A.M. between

$m$ th and

$n$ th terms of the A.P., then show that

$p+q=m+n$ .

Question 10

Show that the sum of the arithmetic means, between two given quantities, equidistant from the beginning and the end is constant.