Question

The sum of first n term of AP is given by the formula Sn=3n^2 +n then its 3rd term is

(a) 14

(b) 16

(c) 22

(d) 42

Solve it in the full form

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Answer 1

Answer:

$\sf (b) \:16$

Given:

$\sf S_{n} = 3 {n}^{2} + n$

$\sf S_{1} = 3(1)^{2} + 1$

$\sf \:\:\:\:= 3 + 1$

$\sf S_{1} \:= 4 \: (nothing \: but \: a = 4)$

$\sf S_{2} = 3(2)^{2} + 2$

$\sf \:\:\:\:\:= 12 + 2$

$\sf S_{2} = 14$

• Then

$\sf a _{2} = S_{2} - S_{1}$

$\sf a _{2} = 14 - 4 = 10$

• Then Common Difference

$\sf d = a_{2} - a_{1}$

$\sf \:\: \:= 10 - 4$

$\sf d = 6$

• Therefore

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

$\sf \:\:\:\:\:\:= 4 + 2(6)$

$\sf \:\:\:\:\:\: = 4 + 12$

$\sf \:\:a_{3} = 16$

Answer 2

Answer:

Answer is 16.. Hope it was helpful