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,

$a=2,d=2.5$

• A. $32$
• B. $33$
• C. $34$
• D. $35$

Answer 1

The correct option is D $35$

Here the first term $a=2$ and common difference $d=2.5$.
Now $a_n=a+(n-1)d$
$\therefore a_1=a=2$
$a_2=a+d=2+2.5=4.5$
$a_3=a+2d=2+2\times 2.5=7$
$a_4=a+3d=2+3\times 2.5=9.5$
$a_5=a+4d=2+4\times 2.5=12$

$\therefore$ series in A.P. is $2,4.5,7,9.5,12,....$

Then, the sum of first five terms is $=2+4.5+7+9.5+12=35$

Or

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

$\therefore S_5$ =$\frac{5}{2}\times \left[2\right(2)+(5-1\left)\right(2.5\left)\right]=35$