Pre math question

Question

Find the value of a for this series: 3 + 2 + 4/3 +8/9 + 16/27 + ...

1. 2/3
2. 3
3. 3/2
4. 1/3

Answer 1

Not sure whether "a" refers to the first term in the series, or the common ratio. Normally "a" refers to the first term. If so, then the first term is 3.

In this case, a = 3.

If "a" refers to the common ratio, then form ratios of each pair of terms as follows:

2 / 3, (4/3) / 2, (8/9) / (4/3), etc.

After simplifying, we get the same value:

2/3, 2/3, 2/3, etc.

In this case, a = 2/3.