Question

What is the sum of the first 19 terms of the sequence 9,2,-5,-12....2SEE ANSWERS

Answer 1

-1026

Step-by-step explanation

The sum of the first n terms in an arithmetic sequence is,

`S_n=(n(a_1+a_n))/(2)`

As we can see, we have to find the nth term of the sequence,

`a_n=a_1+(n-1)d`

In this case, the first term is 9 and the common difference is -7 - note that each term is the previous one minus 7. So the formula for the nth term is,

`a_n=9-7(n-1)`

We have to find the 19th term,

`a_(19)=9-7(19-1)=9-7\cdot18=9-126=-117`

So the sum of the first 19 terms is,

`S_(19)=(19\cdot(9+(-117)))/(2)=(19\cdot(9-117))/(2)=(19\cdot(-108))/(2)=(-2052)/(2)=-1026`

Hence, the sum of the first 19 terms of the given sequence is -1026.