Question

Write the sum of first five terms of the following Arithmetic Progressions where, the common difference $d$ and the first term $a$ are given:

$a=6,d=6$

• A. $88$
• B. $89$
• C. $90$
• D. $91$

Answer 1

The correct option is C $90$

Here the first term $a=6$ and common difference $d=6$.
Now $a_n=a+(n-1)d$
$\therefore a_1=a=6$
$a_2=a+d=6+6=12$
$a_3=a+2d=6+2\times 6=18$
$a_4=a+3d=6+3\times 6=24$
$a_5=a+4d=6+4\times 6=30$
$\therefore$ series in A.P is $6,12,18,24,30,....$

Thus, the sum of first five terms $=6+12+18+24+30=90$

Hence, the answer is $90$.

Or

We can use the formula for sum of A.P $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

$\therefore S_5$ =$\frac{5}{2}\times \left[2\right(6)+(5-1\left)\right(6\left)\right]=90$