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
If $A_{1}, A_{2}, A_{3}, A_{4}$ 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
If $n$ 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
If $\frac{x^{p}+y^{p}}{x^{p-1}+y^{p-1}}$ 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.
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