Question

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

Answer 1

Answer:

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

Option B is correct option.

Step-by-step 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: $S_n=\frac{n}{2}(a_1+a_n)$

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:

$S_n=\frac{n}{2}(a_1+a_n)\\S_{18}=\frac{n}{2}(a_1+a_{18})\\S_{18}=\frac{18}{2}( 23+159)\\S_{18}=9(182)\\S_{18}=1638$

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

Option B is correct option.