# Sequences and Series

## Class 11 NCERT

### NCERT

1   Write the first five terms of the sequences whose $n^{th}$ term is $a_n=n(n+2).$

##### Solution :

$a_n=n(n+2)$$\\ Substituating n=1,2,3,4 and 5, we obtain\\ a_1=1(1+2)=3\\ a_2=2(2+2)=8\\ a_3=3(3+2)=15\\ a_4=4(4+2)=24\\ a_5=5(5+2)=35$$\\$ Therefore, the required terms are $3, 8, 15, 24$ and $35.$

2   Write the first five terms of the sequences whose $n^{th}$ term is $a_n=\dfrac{n}{n+1}$

##### Solution :

$a_n=\dfrac{n}{n+1}$$\\ Substituting n=1,2,3,4,5, we obtain\\ a_1=\dfrac{1}{1+1}=\dfrac{1}{2},a_2=\dfrac{2}{2+1}=\dfrac{2}{3},\\ a_3=\dfrac{3}{3+1}=\dfrac{3}{4},a_4=\dfrac{4}{4+1}=\dfrac{4}{5},\\ a_5=\dfrac{5}{5+1}=\dfrac{5}{6}$$\\$ Therefore, the required terms are $\dfrac{1}{2},\dfrac{2}{3},\dfrac{3}{4},\dfrac{4}{5}$ and $\dfrac{5}{6}$

3   Write the first five terms of the sequences whose $n^{th}$ term is $a_n=2^n$

##### Solution :

$a_n=2^n$$\\ Substituting n=1,2,3,4,5, we obtain\\ a_1=2^1=2\\ a_2=2^2=4\\ a_3=2^3=8\\ a_4=2^4=16\\ a_5=2^5=32$$\\$ Therefore, the required terms are $2, 4, 8, 16$ and $32.$

4   Write the first five terms of the sequences whose $n^{th}$ term is $a_n=\dfrac{2n-3}{6}$