five consecutive terms of an arithmetic sequence have a sum of 40. The product of the middle and the two end terms is 224. Find the terms of the sequence.

Question

anonymous · Answer

5/2(2a+4d)=40
(a+2d)(a+3d)(a+4d)=224
solve for a and d

anonymous · Answer

Lets say the middle term is a and the difference between two terms is d.
Than the first term is a-2d
the 2nd a-d
the 3rd a
4th a+d
5th a+2d
the sum is 5a=40
a=8
the product of 1st 3rd 5th is (8-2d)*8*(8+2d)=224
64-4d^2=28
4d^2=36
d=3 or d=-3
So the terms are
2, 5, 8, 11, 14 or
14, 11, 8, 5, 2

anonymous · Answer

the numbers are 2,5,8,11,14