Question

if the sum of the first n terms of an AP is given by Sn=(3n^2-n), find its 20th term​

Answer 1

sum of the first n terms

$= 3 {n}^{2} - n$

first term = (n = 1)

$3 \times {1}^{2} - 1 \\ = 3 - 1 = 2$

sum of first 2 terms

$= 3 \times {2}^{2} - 2 \\ = 3 \times 4 - 2 \\ = 12 - 2 \\ = 10$

second term = 10 - 2

= 8

common difference = 2nd term - 1st term

d = 8 - 2 = 6

20th term = 1st term + 19d

= 2+ (19×6)

= 2 + 114

= 116

20th term = 116

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