# The Sum of N Natural Number is 5n^2 + 4n. Find Its 8th Term. - Mathematics

#### Question

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

nth term = S_n = S_(n - 1) = 5n^2 + 4n - 5n^2 + 6n - 1 = 10n - 1

=> "8th term" = t_8 = 10 xx 8 - 1 = 80 - 1 = 79

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#### APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 10: Arithmetic Progression
Exercise 10 (C) | Q 13 | Page 144