KC Sinha Mathematics Solution Class 11 Chapter 17 Sequences and Series : AP Exercise 17.1

 Exercise 17.1

Page no -17.3

Question 1

Write the first three terms of the sequences defined by the following :

(i) $t_{n}=3 n+1$

(ii) $2^{n}$

(iii) $t_{n}=n^{2}+1$

(iv) $t_{n}=n(n+2)$

(v) $t_{n}=2 n+5$

(vi) $t_{n}=\frac{n-3}{4}$

(vii) $t_{n}=\frac{2 n-3}{6}$

(viii) $t_{n}=\frac{n}{n+1}$

(ix) $t_{n}=\frac{n^{2}}{n+1}$

(x) $t_{n}=\frac{n\left(n^{2}+5\right)}{4}$

Question 2

Find the indicated terms in each of the following sequences whose $m$ th terms are :

(i) $t_{n}=(-1)^{n-1} 5^{n-1} ; t_{3}$

(ii) $t_{n}=\frac{n^{2}}{2^{n}} ; t_{4}, t_{6}$

(iii) $4 n-3 ; t_{17}, t_{24}$

(iv) $t_{n}=(-1)^{n-1}, n^{3}, t_{9}$

(v) $t_{n}=\frac{n^{2}(n+1)}{3} ; t_{1}, t_{2}$

(vi) $t_{n}=\frac{n(n-2)}{n+3} ; t_{20}$

(vii) $t_{n}=(n-1)(2-n)(3+n) ; t_{20}$

(viii) $t_{n}=\frac{t_{n-1}}{n^{2}}, t_{1}=3 ; t_{2}, t_{3},(n \geq 2)$

Question 3

Write the next three terms of the following sequences :

(i) $t_{2}=2, t_{n}=t_{n-1}+1,(n \geq 3)$

(ii) $t_{1}=3, t_{n}=3 t_{n-1}+2$ for all $n>1$

(iii) $t_{1}=1, t_{n}=\frac{t_{n-1}}{n},(n \geq 2)$

(iv) $t_{1}=t_{2}=2, t_{n}=t_{n-1}-1, n>2$

Question 4

Find the first five terns of the following sequences and write down the corresponding series :

(i) $t_{1}=1, t_{n}=t_{n-1}+2$ for $n \geq 2$

(ii) $t_{1}=-1, t_{n}=\frac{t_{n-1}}{n}, n \geq 2$

Question 5

The Fibonacci sequence is defined by $t_{1}=t_{2}=1_{1}, I_{n}=t_{n-1}+t_{n-2}(n>2)$. If $t_{n+1}=k t_{n}$, then find the values of $k$ for $n=1,2,3$ and 4 .