Question

Find the sum of -5,-1,-3,7up to14terms

Answer 1

Look at the differences of the series as given: 4, 7, 10.

If the series of differences continues as 3n + 1, the next term in the original series will be 37.

So for a quick and dirty answer: go to a spreadsheet and write the series of differences in a column: it starts 4, 7, 10, 13, 16 and ends with 43.

In the next column use the differences to calculate the terms of the series: next term is 37, then 53, 72 ...down to 332.

Then sum up that column which gives 1830 as the sum of the 1st 15 terms.

If you want to be more thorough, the terms of the series given can be calculated as follows:

(3n^2-n+4)/2.

This series can be summed up; it will require a term in n^3.  If you need the expression, please get back to me as it takes more work that I am willing to expend unless you are really stuck!