KC Sinha Mathematics Solution Class 11 Chapter 17 Sequences and Series : AP Exercise 17.2

 Exercise 17.2

Page no 17.12

Type 1

Question 1

If $n$th term of al sequence is $4 n^{2}+1$, find the sequence. Is this sequence at A.P.?

Question 2

If $n$th term of a sequence is $2 a n+b$, where $a, b$ are constants, is this sequence an A.P.?

Question 3

If the $n$th term of a sequence is an expression of first degree in $n$, show that it is an A.P.

Question 4

A sequence $\left\{t_{n}\right\}$ is given by $t_{n}=n^{2}-1, n \in N$. Show that it is not an A.P.

Type 2

Question 5

Find the indicated terms in each of the following arithmetic progression

(i) $1,6,11,16, \ldots, 161$

(ii) $a=3, d=2, t_{n}, t_{10}$

(iii) $5,2,-1, \ldots, t_{10}$

(iv) $a=21, d=-5, t_{n}, t_{25}$

Question 6

Find the 10th term of the sequence $10,5,0,-5,-10, \ldots$

Question 7

Find the 10 th term of the sequence whose 7 th and 12 th terms are 34 and 64 respectively.

Question 8

The $p$ th, $q$ th and $r$ th terms of an A.P. are $a, b, c$ respectively. Show that $(a-b) r+(b-c) p+(c-a) q=0$

Question 9

Find the first negative term of the sequence $999,995,991,987, \ldots$

Question 10

In an A.P. if $m$ th term is $n$ and $n$th term is $m$, where $m \neq n$, find the prh term.

Question 11

Each of the sequences $3,5,7, \ldots$ and $4,7,10, \ldots$ is continued to 100 terms. Find how many terms are identical.

Question 12

Find the number of all positive integers of 3 digits which are divisible by 5.

Question 13

For an A.P. show that (i) $t_{m}+t_{2 n+m}=2 t_{m}+n$

(ii) $t_{m+n}+t_{m-n}=2 t_{m}$

Question 14

Determine the number of terms in the A.P. 3, $7,11, \ldots, 399$. Also find its 200t term from the end.

Question 15

If $\left|t_{n}\right|$ is an A.P. such that $\frac{t_{4}}{t_{7}}=\frac{2}{3}$, find $\frac{t_{8}}{t_{9}}$.

Question 16

Show that the sequence $\log a, \log (a b), \log \left(a b^{2}\right), \log \left(a b^{3}\right), \ldots$ is an A.R. Find its $n$th term.

Question 17

A man starts repaying a loan as first instalment of Rs. 100 . If he increases the instalment by Rs. 5 every month. what amount he will pay in the 3ocht instalment ?

Page no 17.13

Type 3

Question 18

Three numbers are in A.P. their sum is 27 and the sum of their squares is $275 .$ Find the numbers.

Question 19

The sum of three number in A.P is 12 and the sum of their cubes is 408 . Find the numbers 

Question 20

Divide 15 into three parts which are in A.P and the sum of their squares is 83/

Question 21

Divide 20 into four parts which are in A.P . Such that the product of the first and fourth is to the product of the second and third is 2: 3