Question

Find the sum of first 51 terms of an A. P. whose $2^{nd}$ and $3^{nd}$ terms are 14 and 18 respecitively.

Answer 1

$a_2$ = 14 and $a_3$ = 18
Common difference = $a_3$ - $a_2$ = 18 - 14 = 4 = d
Now
$a_2$ = a + d = 14
a + 4 = 14
a = 10
Now, sum of 51 terms
= $\frac{51(2a+(50\left)d\right)}{2}$
= $\frac{51(20+200)}{2}$
= $\frac{51\times 220}{2}$
= 51×110 = 5610
Therefore sum of 51 terms is 5610