Question

Find the fourth term of ap if nth term sum is 5n^2+6n

Answer 1

$\bold{Answer :}$

Given that, sum of nth terms,

Sₙ = 5n² + 6n

∴ the nth term be

= Sₙ - Sₙ_₁

= (5n² + 6n) - {5 (n - 1)² + 6 (n - 1)}

= 5n² + 6n - {5 (n² - 2n + 1) + 6n - 6}

= 5n² + 6n - (5n² - 10n + 5 + 6n - 6)

= 5n² + 6n - (5n² - 4n - 1)

= 5n² + 6n - 5n² + 4n + 1

= 10n + 1

∴ the 4th term of the AP be

= 10 (4) + 1

= 40 + 1

= 41

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