Question

the sum of 1st n terms of an AP is given by the formula Sn=3n^2+n, then its 3rd term is ​

Answer 1

$\sf\large\bold{\underline{\pink{SoLuTiOn}}}$

$\sf{S_{n} = 3n² + n}$

Put n = 1

3(1)² + 1

⇒ $\sf\bold\blue{4 = a_{1} }$ ••••• (i)

Put n = 2

3(2)² + 2

⇒ $\sf\bold\blue{14 = a_{1} + a_{2} }$ ••••• (ii)

Solving equation (i) and (ii)

We get,

$\sf{a_{1} = 4}$

$\sf{a_{2} = 10}$

Common difference (d) = $\sf{a_{2} - a_{1}}$ = 10 - 4 = 6

3rd Term = $\sf{a_{3} = a + 2d}$

⇒ 4 + 2 × 6

⇒ 4 + 12

⇒ 16

$\sf\bold\pink{a_{3} = 16}$