Question

How do you find the 10th partial sum of the arithmetic sequence `8, 20, 32, 33,...`?

Answer 1

`S_10=400`

Explanation:

For the sake of your question, let's assume your arithmetic sequences followed this pattern instead:
`8, 20, 32, 44` (not `33`)

Note the difference, `d=12`

The formula for the sum of `n` terms is

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

Where `a_1=8` and `n=10`. This gives us

`S_10=10/2(8+a_(10))=5(8+a_(10))`

Next, find the formula for `a_n`

`a_n=a_1+(n-1)d`
`a_n=8+(n-1)12`
`a_n=8+12n-12`
`a_n=12n-4`

So, with `n=10`, we have `a_10=12(10-4)=72`

Therefore, `S_10=5(8+72)=400`