Question

what is the sum of the finite arithmetic series? (-5)+0+5+10+....+65


900.A)
455.B)
450.C)
445.D)

Answer 1

Okay, well, the sum of an arithmetic series is \[\frac{n(a_1+a_n)}{2}=S_n\] Where n is the number of terms in the series, a(1) is the first term and a(n) is the nth term.

Answer 2

nth term?

Answer 3

i.e. the number of terms you want to find. So if you only wanted -5, 0, 5, 10, 15 n=5 and a(n) would be 15 (the 5th term in the sequence)

Answer 4

oh ok

Answer 5

Okay, so you know a(1) and a(n) right? Now you just need to determine how many terms are in that sequence from -5 until 65.
So, to do that you'll want to know how much you are adding to the series each time.

Answer 6

which is 5

Answer 7

Yes. So, how can you use that to find the number of terms in the sequence from -5 to 65?

Answer 8

add it, from 15 its 11 to get to 65 but then what

Answer 9

Plug the number of terms you get into the equation for n. -5 for a(1) and 65 for a(n)
And a hint for arithmetic sequences since it is always adding the same number each time, you can just divide the n-th term by the number you add each time if you have 0 in the set. So 65/5 = 13 (that would be all the terms from 5 to 65) then just add 2 more to that for 0 and -5