Question

Find the sum of the first $15$ terms of the following sequence having $n$th term as
$a_n=3+4n$

• A. 525
• B. 563
• C. 184
• D. 189

Answer 1

The correct option is A 525

$a_n=3+4n$ (Given)

Now,

$a_1=3+4\times 1=7$

$a_2=3+4\times 2=11$

$a_3=3+4\times 3=15$

So the series is

The sum of first is turns is

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$a=7,n=15,d=4$

$S_n=\frac{15}{2}[2\times 7+(15-1\left).4\right]$

$S_n=\frac{15}{2}[14+56]$

$S_n=\frac{15\times 70}{2}$

$S_n=15\times 35$

$S_n=525$

The sum of first $15$ terms of given series is

$S_n=525$