Question

Just 15

Determine whether the series is arithmetic or geometric, the find the indicated sum. Please help ASAP

Answer 1

Really hard to make it out, especially the upper limit of the sum, but I think it reads

`\displaystyle\sum_(k=1)^n5k-42`

(not sure what
`n` is, but that's not very important)

Expand the sum as

`\displaystyle5\sum_(k=1)^nk-42\sum_(k=1)^n1`

Recall that

`\displaystyle\sum_(k=1)^n1=1+1+\cdots+1=n`

`\displaystyle\sum_(k=1)^nk=1+2+\cdots+n=\frac{n(n+1)}2`

so that

`\displaystyle\sum_(k=1)^n5k-42=\frac{5n(n+1)}2-42n`

Then just plug in whatever
`n` happens to be.