From: Forrest, a secondary school student

I'm having a little trouble with these arithmetic and geometric
sequence problems and I was hoping you could help me. They are similar
problems, one deals with arithmetic sequences and the other deals with
geometric sequences.

1) Find three successive terms in an arithmetic sequence such that their sum
is 24 and their product is 440

2) Find three successive terms in a geometric sequence such that their sum
is 21 and their product is 216




Hi Forrest,

I'll give you some help on the first problem. The sequence is arithmetic so let's suppose that the first of your three terms id k and the common difference is d. The three terms are then

k, k + d and k + 2d

Hence the sum of the three terms, which is 24, is given by

k + k + d + k + 2d = 24 thus
3k + 3d = 24, so
k + d = 8 or d = 8 - k

The product of the three terms is 440 so

k(k + d)(k + 2d) = 440

Substitute d = 8 - k and solve for k.

Use the same technique for the second problem but using the fact that the sequence is geometric not arithmetic.