Question

Find the ${20}^{th}$ term and sum of the 20 term of the series 1, 4, 7, 10....

• A. 58, 490
• B. 58, 590
• C. 59, 590
• D. 59, 490

Answer 1

The correct option is B

58, 590

Given series 1, 4, 7, 10......
This series is an AP
$n^{th}$ term $t_n=a+(n-1)d$
${20}^{th}$ term $t_{20}=1+(20-1)3$
=1+57=58
Sum of the n terms $s_n=\frac{n}{2}[2a+(n-1\left)d\right]$
To find the sum of 20 terms substitute n=20

$s_{2}0=\frac{{20}^{10}}{2}[2\times 1+(19\times 3\left)\right]$
=590