arithmetic progression,any good idea?

[elenis297]

If the sum of the 4th term and the 12th term of an arithmetic progression is 8, what is the sum of the first 15 terms of the progression?

[RonPurewal]

ok, you're supposed to cite the original source, but this problem is generic enough to address.

are the answer choices numbers?
if so, all you have to do is find one example, since any valid example has to give the same answer as any other valid example.

one example that's particularly easy to find here is 4, 4, 4, 4, ...
there you go. it's the sum of fifteen 4's.

[RonPurewal]

as far as the theory underlying the question:

• with an "arithmetic progression",** the numbers are equally spaced. so, the average is the same as whatever number is in the middle.

• think about which number represents the average of the 4th and 12th terms.

• now, think about which number represents the average of the 1st through 15th terms.

that should be enough to get you started on discovering how this works (although, as pointed out above, you really don't have to-- you can just take all 4's).

[RonPurewal]

forgot the footnote

**the GMAT will NOT require you to know this term. if they use it, they'll define it (as they do in OG multiple-choice #126).

[Binit]

as far as the theory underlying the question:

• with an "arithmetic progression",** the numbers are equally spaced. so, the average is the same as whatever number is in the middle.

• think about which number represents the average of the 4th and 12th terms.

• now, think about which number represents the average of the 1st through 15th terms.

that should be enough to get you started on discovering how this works (although, as pointed out above, you really don't have to-- you can just take all 4's).

Hi Ron, that's excellent thinking. However, I started with formulae: a+3d+a+11d = 8. so, 2a+14d = 8. so, S(15) = 15/2(2a+14d) = 15/2*8 = 60.
but, only after reading ur answer I realized that every time I calculate the sum of an AP, I basically multiply the middle term with n.
Thanks.

[RonPurewal]

i don't know those formulas, but it seems you're using 'a' = first term and 'd' = difference.

you're never going to NEED a formula for something like this, but it can't hurt.
basically, more options = better.