Question

4. Find the sum of the first eighteen terms of the arithmetic sequence whose nth

term is an = 15 + 8n.
a. 1438
b. 1638
c. 1836
d. 1783​

Answer 1

The sum of first eighteen terms of the arithmetic sequence is
`\mathbf{S_(18)=1638}`

Option B is correct option.

Explanation:

We need to find the sum of the first eighteen terms of the arithmetic sequence whose nth term is an = 15 + 8n

The formula used to calculate sum of arithmetic sequence is:
`S_n=(n)/(2)(a_1+a_n)`

Finding a₁ by putting n=1

`a_n=15+8n\\a_(1)=15+8(1)\\a_(1)=15+8\\a_(1)=23`

We have
`a_1=23`

Finding 18th term n=18

`a_n=15+8n\\a_(18)=15+8(18)\\a_(18)=15+144\\a_(18)=159`

So, the sum of first eighteen terms of the arithmetic sequence is:

`S_n=(n)/(2)(a_1+a_n)\\S_(18)=(n)/(2)(a_1+a_(18))\\S_(18)=(18)/(2)( 23+159)\\S_(18)=9(182)\\S_(18)=1638`

So, the sum of first eighteen terms of the arithmetic sequence is
`\mathbf{S_(18)=1638}`

Option B is correct option.