Question

Evaluate the sum from n equals five to nine of quantity three n plus two

Answer 1

Answer:

The given expanded sum of the series is $\sum\limits_{n=5}^{9}3n+2=115$

Step-by-step explanation:

Given problem can be written as

$\sum\limits_{n=5}^{9}3n+2$

To find their sums:

Now expanding the series

That is put n=5,6,7,8,9 in the given summation

$\sum\limits_{n=5}^{9}3n+2=[3(5)+2]+[3(6)+2]+[3(7)+2]+[3(8)+2]+[3(9)+2]$

$=[15+2]+[18+2]+[21+2]+[24+2]+[27+2]$

$=17+20+23+26+29$  (adding the terms)

$=115$

Therefore $\sum\limits_{n=5}^{9}3n+2=115$

Therefore the given sum of the series is $\sum\limits_{n=5}^{9}3n+2=115$

The given expanded sum of the series is $\sum\limits_{n=5}^{9}3n+2=115$