Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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

Sagot :

ANSWER

-1026

EXPLANATION

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

[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]

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

[tex]a_n=a_1+(n-1)d[/tex]

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,

[tex]a_n=9-7(n-1)[/tex]

We have to find the 19th term,

[tex]a_{19}=9-7(19-1)=9-7\cdot18=9-126=-117[/tex]

So the sum of the first 19 terms is,

[tex]S_{19}=\frac{19\cdot(9+(-117))}{2}=\frac{19\cdot(9-117)}{2}=\frac{19\cdot(-108)}{2}=\frac{-2052}{2}=-1026[/tex]

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

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.