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 as:

$a=3,d=4$

• A. $50$
• B. $55$
• C. $60$
• D. $65$

Answer 1

The correct option is B $55$

Here the first term $a=3$ and common difference $d=4$.
Now $a_n=a+(n-1)d$
Therefore,

$a_1=a=3$
$a_2=a+d=3+4=7$
$a_3=a+2d=3+2\times 4=11$
$a_4=a+3d=3+3\times 4=15$
$a_5=a+4d=3+4\times 4=19$
$\therefore$ series in A.P. is $3,7,11,15,19,......$

Thus, the sum of first five terms $=3+7+11+15+19=55$

Hence, the answer is $55$.

Or

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

$\therefore S_5$ =$\frac{5}{2}\times \left[2\right(3)+(5-1\left)\right(4\left)\right]=55$