#### Question

The sum of n natural number is `5n^2 + 4n`. Find its 8^{th} term.

#### Solution

Sum of n natural numbers `S_n = 5n^2 + 4n`

=> Sum of (n - 1) natural numbers = `S_(n - 1) = 5(n - 1)^2 + 4(n - 1)`

`= 5(n^2 + 1 - 2n) + 4n - 4`

`= 5n^2 + 5 - 10n + 4n - 4`

`= 5n^2 - 6n + 1`

n^{th} term = `S_n = S_(n - 1) = 5n^2 + 4n - 5n^2 + 6n - 1 = 10n - 1`

`=> "8^{th} term" = t_8 = 10 xx 8 - 1 = 80 - 1 = 79`

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The Sum of N Natural Number is 5n^2 + 4n. Find Its 8th Term. Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms..

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