Question

Use sigma notation to represent the sum of the first eight terms of the following sequence: 4,7. 10,

Answer 1

To answer this question, we need to check the kind of sequence here. We have that the first three elements of the sequence are:

`4,7,10`

If we have the difference between the second element and the first element, and the difference between the third element and the second element, we have:

`7-4=3,10-7=3`

Thus, we have a common difference of 3. This is an arithmetic sequence. Then, we also have that:

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

This is the formula for finding a general term in an arithmetic sequence, where:

• an is any term, n, in the sequence.

,

• a1 is the first term in the sequence.

,

• n the number of the term in the sequence.

,

• d is the common difference of the sequence.

In this way, we have:

a1 = 4

d = 3