Question

Find the sum of the first 25 terms of the A.P.: 2 + 5 + 8 + 11 + ............ (use Gauss method)

• A. 910
• B. 930
• C. 950
• D. 940

Answer 1

The correct option is C 950

Given that $a=2;d=3$
$n=25;a_{25}=$?
Using Gauss method, we find the value of $a_{25}$
$a_n=a+(n-1)d$
$a_{25}=2+(25-1)3$
$=2+\left(24\right)3$
$a_{25}=74$
Sum of 'n' series using Gauss method is,
$S_n=\frac{n}{2}$ [First term + Last term]
$=\frac{25}{2}[2+74]$
$=12.5\left(76\right)$
$S_n=950$