Question

Sum of 1st nth term = 1/2(3n²+7n) find nth term and 20th term

Answer 1

$\bold{Answer :}$

Given that, sum of 1st nth terms

Sₙ = 1/2 (3n² + 7n)

∴ the nth term

= Sₙ - Sₙ_₁

= 1/2 (3n² + 7n) - 1/2 {3 (n - 1)² + 7 (n - 1)}

= 1/2 [3n² + 7n - 3 (n² - 2n + 1) - (7n - 7)]

= 1/2 [3n² + 7n - 3n² + 6n - 3 - 7n + 7]

= 1/2 (6n + 4)

= 2/2 (3n + 2)

= 3n + 2

∴ the 20th term be

= 3 (20) + 2

= 60 + 2

= 62

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