Question

if sum of n terms of an ap is 2n^2+5n, then its nth term is​

Answer 1

Nth term of AP is $t_n = 7 + 4n -4$.

• Sum of n terms of AP is given by $S_n = \frac{n}{2}[2a + (n-1)d]$ , where a is first term, dis common difference and n is the number of terms.
• But sum of n terms of AP is given as $2n^{2}  + 5n$.

Therefore,

$S_n = \frac{n}{2}[2a + (n-1)d]$ = $2n^{2}  + 5n$

$na + \frac{n^{2}d }{2} -\frac{nd}{2} = 2n^{2} + 5n$

• Comparing both sides,

a - $\frac{d}{2}$ = 5 .....(Equation 1)

$\frac{d}{2} = 2$

d = 4

• Substituting the value of d in equation 1, we get

a - $\frac{4}{2}$ = 5

a - 2 = 5

a = 7

• We have to find the nth term of AP,

• We have the formula, $t_n = a +(n-1)d$

$t_n = 7 +(n-1)4$

$t_n = 7 + 4n -4$