Question

The sum of n natural numbers is 5n^2+4n.find its 8th term

Answer 1

this is ur required result

Answer 2

The value of $S_{8}$ is 79.

To find:

Find the value of 8th term of the given series.

Solution:

Given that  $S_{n}=5 n^{2}+4 n$

Let us assume that the n =8,  

$S_{8}=(5 \times 8 \times 8)+(4 \times 8)$

=320+32

=352

$S_{8}$ refers the sum of the first 8 numbers of the given sequence, which is equal to the value of 352.

$S_{7}$ refers the sum of the first 7 numbers of the given sequence, which is equal to the value of 273.

For n =7,  

$S_{7}=(5 \times 7 \times 7)+(4 \times 7)$

= 245+28  

= 273.

By subtracting the sum of first 8 numbers by the sum of first 7 numbers to get the value of $S_{8}$.

$\begin{array}{c}{S_{1}+S_{2}+S_{3}+S_{4}+S_{5}+S_{6}+S_{7}+S_{8}=352} \\ {-S_{1}+S_{2}+S_{3}+S_{4}+S_{5}+S_{6}+S_{7}=273}\end{array}$

$S_{8}=79$

Therefore the term $S_{8}=79$