Question

Find the ${20}^{th}$ term of the series 3 + $\frac{1}{2}$(3 + 5) + $\frac{1}{3}$(3 + 5 + 7) + $\frac{1}{4}$(3 + 5 + 7 + 9) + .........

• A. 20
• B. 21
• C. 22
• D. 23

Answer 1

The correct option is C

22

$n^{th}$ term of the above-given series can be written as

$T_n$ = $\frac{\sum (2n+1)}{n}$

= $\frac{2\sum n+\sum 1}{n}=\frac{\frac{2.n(n+1)}{2}+n}{n}$

= $\frac{n\left[\right(n+1)+1]}{n}=n+2$

20th term = 20 + 2 = 22