Answer:
[tex]S_n=[/tex] -348
Step-by-step explanation:
We are given the following arithmetic sequence and we are to find the sum of its first 12 terms:
1, -4, -9, -14, . . .
For that, we will use the formula for the sum of the arithmetic mean:
[tex]S_n=\frac{n}{2} (a_1+a_n)[/tex]
We know the value of the first term ([tex]a_n[/tex]) but we need to find the value of [tex]a_{12}[/tex]. So we will use the following formula:
[tex]a_{12}=a_1+(n-1)d[/tex]
[tex]a_{12}=(-4)+(12-1)(5)[/tex]
[tex]a_{12}=-59[/tex]
Substituting these values in the sum formula to get:
[tex]S_n=\frac{12}{2} (1+(-59))[/tex]
[tex]S_n=[/tex] -348
