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Ronch [10]
3 years ago
8

Find the indicated sum of each sequence S8 of -2,-13,-24,-35

Mathematics
1 answer:
valentina_108 [34]3 years ago
3 0

Answer:

The sum of the arithmetic sequence is S_{8}=-324.

Step-by-step explanation:

A sequence is a set of numbers that are in order.

In an arithmetic sequence the difference between one term and the next is a constant.  In other words, we just add the same value each time infinitely.

If the first term of an arithmetic sequence is a_1 and the common difference is d, then the nth term of the sequence is given by:

                                                  a_{n}=a_{1}+(n-1)d

For the sequence

                                                -2,-13,-24,-35,...

The pattern is continued by adding -11 to the last number each time.

An arithmetic series is the sum of an arithmetic sequence.  We find the sum by adding the first, a_1 and last term, a_n, divide by 2 in order to get the mean of the two values and then multiply by the number of values, <em>n</em>

<em>                                                     </em>S_{n}=\frac{n}{2}(a_{1}+a_{n})<em />

The sum of the arithmetic sequence is

a_{8}=-2+(8-1)(-11)=-2-77=-79

S_{8}=\frac{8}{2}(-2-79})=4\left(-2-79\right)=4\left(-81\right)=-324

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