Question

PLEASE HELP WILL GIVE MEDAL

Write the sum using summation notation, assuming the suggested pattern continues

-9 - 4 + 1 + 6 + ... + 66

Answer 1

You need to try out combinations. It's a good idea to try to find a constant relationship between terms. over here we have
-4 = -9 + 5
1 = -4 + 5
6 = 1 + 5
and in general if the current term is a, the next is a+5, then a + 2*5, a+ 4*5... a + i * 5
In this case we start the series with a = -9

so we have -9 + i * 5, if we let i = 0, we have -9, so that's the starting index and since 66 = -9 + 75 and 75 = 5 * 19 we have the last index being 19.

bringing it all together you have \[\sum_{i =0}^{19}-9 + 5*i\]

Answer 2

Thanks!