Given that the sum of the first three terms of a sequence is 48, and the product of those three terms is 2496, what is the fourth term of the sequence?
I can manage to show my work until
#16 =a+d# ,
but I'm unsure about how to get further without guessing and checking.
I can manage to show my work until
but I'm unsure about how to get further without guessing and checking.
1 Answer
Explanation:
I'm going to assume that you are referring to an arithmetic sequence, where the difference between consecutive terms of the sequence is constant.
Suppose that the first term is
The sum of the first three terms is then
which you correctly derived.
Now, the problem further gives that the product of the first three terms is
It may seem that the above equation is too difficult to solve. However, recall that you have already derived that
Now, again using the fact that
Factor the quadratic equation:
Thus, we have
So there are two possible sequences that satisfy the constraints defined in the problem:
I'll leave it up to you to verify that these two series indeed work. Thus, you have the two possible answers of