Question

The sum of n terms of an AP is n(3n+5), find the 5th term of an AP

Answer 1

Answer:

The sum of n terms of an AP is n(3n+5), then 5th term of an AP is 32

Step-by-step explanation:

Given that, sum of first n terms of an AP is n(3n + 5).

So,

$\sf \: S_n = n(3n + 5)$

$\implies\sf \: \sf \: S_n = {3n}^{2} + 5n$

We know,

$\sf \: T_n = S_n - S_{n - 1}$

On substituting n = 5, we get

$\sf \: T_5 = S_5 - S_{4}$

$\sf \: T_5 = [ 3 {(5)}^{2} + 5(5)] - [ 3 {(4)}^{2} + 5(4)]$

$\sf \: T_5 = (75 + 25) - (48 + 20)$

$\sf \: T_5 = 100 - 68$

$\implies\sf \: \sf \: T_5 = 32$

Hence, The sum of n terms of an AP is n(3n+5), then 5th term of an AP is 32

$\rule{190pt}{2pt}$

Additional Information:

↝ nᵗʰ term of an arithmetic progression is,

$\begin{gathered}\bigstar\:\:{\underline{{\boxed{\sf{{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}$

↝ Sum of n  terms of an arithmetic progression is,

$\begin{gathered}\bigstar\:\:{\underline{{\boxed{\sf{{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

a is the first term of the progression.

n is the no. of terms.

d is the common difference.