Question

Write the sum of the first five terms of the Arithmetic Progression for which the common difference $d$ and the first term $a$ are given below:

$a=5,d=2$

• A. $40$
• B. $45$
• C. $50$
• D. $55$

Answer 1

Answer: (B)

$45$

Given: the first term $a=5$ and common difference $d=2$.
Now $a_n=a+(n-1)d$
$\therefore a_1=a=5$
$a_2=a+d=5+2=7$
$a_3=a+2d=5+2\times 2=9$
$a_4=a+3d=5+3\times 2=11$
$a_5=a+4d=5+4\times 2=13$
$\therefore$ The series in A.P. is $5,7,9,11,13,.....$

Sum of the first five terms is $=5+7+9+11+13=45$

Hence, the answer is $45$.

Or

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

$\therefore S_5$ =$\frac{5}{2}\times \left[2\right(5)+(5-1\left)\right(2\left)\right]=45$