Question

if the sum of first n terms of an ap is 4+3n find its fourth term

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If $a_n$ is the ${n}^{th} \:$term

and $S_n \:$is the sum of first n terms an Arithmetic progression

Then $a_n \: = S_n \: - S_{n - 1} \:$

GIVEN

The sum of first n terms of an AP is 4+3n

TO DETERMINE

The fourth term of the AP

EVALUATION

Here $S_n \: = 4 + 3n$

So

$S_4 \: = 4 + (3 \times 4) = 4 + 12 = 16$

$S_3\: = 4 + (3 \times 3) = 4 + 9 = 13$

Hence Fourth term of AP is

$a_4 \: = S_4 \: - S_3 \: = 16 - 13 = 3$

$\red{ \fbox{FOURTH TERM \: = \: 3 \: }}$