Answer:
528
Step-by-step explanation:
We are given the following sequence:
31,41,51,61,71,81,91,101
Count the terms and see that there are 8 terms total.
If you notice, each terms add up by 10.
31+10 = 41
41+10 = 51
51+10 = 61
Therefore, this is an arithmetic sequence with 10 as common difference.
To find the sum of 8 sequences, we will be using the following formula.
[tex] \displaystyle \large{S_n = \frac{1}{2} n(a_1 + a_n)}[/tex]
We know that:
- There are 8 terms total. (n = 8)
- Our first term is 31 (a1 = 31)
- Our last term is 101 (an = 101)
Substitute the following in the sum formula.
[tex] \displaystyle \large{S_8 = \frac{1}{2} (8)(31+ 101)} \\ \displaystyle \large{S_8 = 4(132)} \\ \displaystyle \large{S_8 = 528}[/tex]
Therefore, the sum of all 8 sequences is 528.
