KC Sinha Mathematics Solution Class 11 Chapter 17 Sequences and Series : AP Exercise 17.3

 Exercise 17.3

Page no 17.21

Question 1

If the sum to $n$ terms of a sequence is $2 n^{2}+4$. Find its $n$th term. Is this sequence an A.P. ?

Question 2

Find the sum of the following series :

(i) $1+4+7+10+\ldots$ to 40 terms

(ii) $2+3 \frac{1}{3}+4 \frac{2}{3}+\ldots$ to 60 terms

(iii) $\frac{3}{\sqrt{5}}+\frac{4}{\sqrt{5}}+\sqrt{5}+\ldots$ to 25 terms

(iv) $1+5+3+9+5+13+7+\ldots$ to 20 terms.

Question 3

How many terms of the series $15+12+9+\ldots .$ must be taken to make 15 ? Explain the double answers.

Question 4

(i) Find the sum of all the odd numbers lying between 100 and 200 .

(ii) Find the sum of all odd integers from 1 to 2001 .

Question 5

Determine sum of first 35 terms of an A.P. if second term is 2 and the seventh term is 22 .

Question 6

If the sum of first $p$ terms of an A.P. is $q$ and the sum of first $q$ terms is $p$. then find the sum of $(p+q)$ terms.

Question 7

How many terms of the A.P. $-6,-\frac{11}{2},-5, \ldots$ are needed to give the sum $-25$ ?

Question 8

Solve for $x$ :

(i) $1+6+11+16+\ldots+x=148$

(ii) $25+22+19+16+\ldots+x=115$

Question 9

(i) Find the sum of all integers from 1 to 100 which are multiples of 2 or 5 .

(ii) Find the sum of all natural numbers lying between 100 and 1000 which are multiples of 5 .

Question 10

Find the sum of all integers between 200 and 400 which are divisible by 7 .

Question 11

If the sum to $n$ terms of a sequence be $n^{2}+2 n$, then prove that the sequence is an $A . P .$

Question 12

(i) Find the sum to $n$ terms of an A.P. whose $k$ th term is $5 k+1$.

(ii) Find the sum of all numbers of two digits which leaves the remainder 1 when divided by 4 .

Question 13

If the sum of $n$ terms of an A.P. is $3 n^{2}+5 n$ and its $m$ th term is 164 , find the value of $m$

[Hint : $\left.t_{m}=S_{m}-S_{m-1}=3 m^{2}+5 m-3(m-1)^{2}-5(m-1)=6 m+2\right]$

Question 14

If the sum of $n$ terms of an A.P. is $p n+q n^{2}$, where $p$ and $q$ are constants, find the common difference.

Question 15

If the sum of $n$ terms of an A.P. is $n P+\frac{1}{2} n(n-1) Q$. where $P$ and $Q$ are constants, find the common difference of the A.P.

Question 16

If the sum of 8 terms of an A.P. is 64 and the sum of 19 terms is 361 , find the sum of $n$ terms.

Question 17

If $a, b, c$ be the 1st, 3 rd and $n$th terms respectively of an A.P., prove that the sum to $n$ terms is $\frac{c+a}{2}+\frac{c^{2}-a^{2}}{b-a}$.

Question 18

If the $m$ th term of an A.P. is $\frac{1}{n}$ and the $n$th $\operatorname{term}$ is $\frac{1}{m}$, then prove that the sum to $m$ terms is $\frac{m n+1}{2}$, where $m \neq n$