Question

Find the sum of the first 30 terms of the sequence below an=3n+2

Answer 1

first off, let's find the 1st term's value, and the 30th term's value,


`\bf a1=3(1)+2\implies a1=5\qquad \qquad \quad a30=3(30)+2\implies a30=92\\\\ -------------------------------\\\\ ~~~~~~~\textit{ Sum of an arithmetic sequence}\\\\ S_n=\cfrac{n(a1+an)}{2}~ \begin{cases} n=n^(th)\ term\\ a1=\textit{first term's value}\\ ----------\\ a1=5\\ a30=92\\ n=30 \end{cases} \implies S_(30)=\cfrac{30(5+92)}{2} \\\\\\ S_(30)=15(97)`

Answer 2

`S_(30)`= 1455.

Explanation:

Given : an=3n+2.

To find : find the sum of the first 30 terms of the sequence.

Solution : We have given
`a_(n)` = 3n + 2.

For first term n = 1

`a_(1)` = 3 (1) +2.

`a_(1)` = 5

For last term n = 30

`a_(30)` = 3(30) +2

`a_(30)` = 90 +2

`a_(30)` = 92.

Then sum of first 30 terms

`S_(30) =(n(First\ term+last\ term))/(2)`.

`S_(30) =(30(5+92))/(2)`.

`S_(30) =(30(97))/(2)`.

`S_(30)`= 15 *97.

`S_(30)`= 1455.

Therefore,
`S_(30)`= 1455.