Question

Find the sum of the first 4 terms of the sequence 4,8,12,16,20,........

• A. 30
• B. 20
• C. 40
• D. 60

Answer 1

The correct option is C 40

Consider the sequence 4, 8, 12, 16, 20 ...
$⟹\text{First term of the AP,}a=4$ and $\text{Common difference}=d=a_2-a_1=8-4=4$

The sum upto $n$ terms of the AP is given by:
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Thus, the sum upto 4 terms of the given AP is:
$S_4=\frac{4}{2}[2\times 4+(4-1\left)4\right]$
$=2\times [8+(3\times 4\left)\right]$
$=2\times [8+12]$
$=2\times 20$
$=40$
Thus, the sum upto 4 terms of the AP is 40.

Aliter:
$4+8+12+16=4(1+2+3+4)=4\times \frac{4\times 5}{2}(\because 1+2+3+...+n=\frac{n(n+1)}{2})=40$