Question

What is the sum of a 30-term arithmetic sequence where the first term is 72 and the last term is -102?

Answer 1

Hint:

The formula is

S = n*(first term + last term)/2

where S is the sum of the first n terms and n is the number of terms

Answer 2

so , s = 30*(72-102)/2 .

Answer 3

that is correct

Answer 4

keep going and tell me what you get

Answer 5

-450 ?

Answer 6

i'm getting that as well

Answer 7

awesome :) thanks !

Answer 8

you're welcome

Answer 9

alternatively (not the best alternative, but it's still out there) you can do this


72+66+60+54+48+42+36+30+24+18+12+6+0+(-6)+(-12)+(-18)+(-24)+(-30)+(-36)+(-42)+(-48)+(-54)+(-60)+(-66)+(-72)+(-78)+(-84)+(-90)+(-96)+(-102) = -450


Basically, generate 30 terms by repeatedly subtracting 6 from them to get 30 terms (first term is 72 and last term is -102). Then add them all up. You'll see that the answer is still -450


This is a long method, so the first method is definitely preferred.

Answer 10

i tried that the first time but came up with the wrong answer ... probably a simple adding error on my part .

Answer 11

that's probably the case

I had a program help me generate all the terms which is why I was able to do it accurately...even then it gets a bit ugly