Question

find the sum of aps 2,7,12, .... 20 term ​

Answer 1

Given :

AP = 2,7,12

To find :

Sum of first 20 terms

Formula used :

$\sf \bullet\: \: Common \:difference\: (d)\: = \: T_2 \:-\: T_1\\\\ \sf \bullet \: S_n \: = \dfrac{n}{2}\times [ 2T_1 \:+\:(n-1)d\:]$

Solution :

First of all we need to find common difference (d)

d= 7 -2 = 5

$\sf \implies \: \: S_n \: = \dfrac{n}{2}\times [ 2T_1 \:+\:(n-1)d\:] \\ \\ \sf \implies \: \: S_n \: = \: \dfrac{20}{2} \times [ \: (2 \times 2) \: +\:(20 - 1)5\:] \\ \\ \sf \implies \: \: S_n \: = \: 10 \times [ \: (4) \: +\:(19)5] \\ \\ \sf \implies \: \: S_n \: = \: 10(4 + 95) \\ \\ \sf \implies \: \: S_n \: = \: 10(99) \\ \\ \sf \implies \: \: S_n \: = \:990$

ANSWER : 990