Question

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

Answer 1

Given that, the sum of the first n Natural numbers.

$S_n$ = 5$n^2$ + 4n

Now,

$S_8$ = 5 ${\left(8\right)}^2$ + 4 (8)

= (5 $\times$ 64) + 32

= 320 + 32

= 352

and

$S_7$ = 5 ${\left(7\right)}^2$ + 4 (7)

= 5 (49) + 28

= 245 + 28

= 273

Thus, the 8th term is

= $S_8$ - $S_7$

= 352 - 273

= 79