Answer:
The sum of first eighteen terms of the arithmetic sequence is [tex]\mathbf{S_{18}=1638}[/tex]
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: [tex]S_n=\frac{n}{2}(a_1+a_n)[/tex]
Finding a₁ by putting n=1
[tex]a_n=15+8n\\a_{1}=15+8(1)\\a_{1}=15+8\\a_{1}=23[/tex]
We have [tex]a_1=23[/tex]
Finding 18th term n=18
[tex]a_n=15+8n\\a_{18}=15+8(18)\\a_{18}=15+144\\a_{18}=159[/tex]
So, the sum of first eighteen terms of the arithmetic sequence is:
[tex]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[/tex]
So, the sum of first eighteen terms of the arithmetic sequence is [tex]\mathbf{S_{18}=1638}[/tex]
Option B is correct option.
