Question

the nth term of an AP is defined as An= 3+4n find the sum of 20 terms​

Answer 1

EXPLANATION.

Nth term of an Ap = 3 + 4n.

To find sum of 20 terms.

→ 3 + 4n

→ put n = 1 → 3 + 4(1) = 7.

→ put n = 2 → 3 + 4(2) = 11.

→ put n = 3 → 3 + 4(3) = 15.

→ put n = 4 → 3 + 4(4) = 19.

Series of an Ap = 7,11,15,19..........n terms.

First term = a = 7.

Common difference = d = b - a = 11 - 7 = 4.

Sum of Nth terms of an Ap.

$\sf \: \implies \: s_{n} \: = \dfrac{n}{2} (2a \: + (n - 1)d$

$\sf \: \implies \: s_{20} \: = \dfrac{20}{2} (2 \times 7 + 19 \times 4) \\ \\ \sf \: \implies \: s_{20} \: = 10(14 + 76) \\ \\ \sf \: \implies \: s_{20} = 10(90) \\ \\ \sf \: \implies \: s_{20} = 900$