Answer:
- common ratio: x^2
- value of x: ±1/2
Explanation:
(a) The ratio of adjacent terms is ...
x^4/x^2 = x^2
The common ratio is x^2.
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(b) For a geometric sequence with ratio r and first term "a", the sum to infinity is ...
S = a/(1 -r)
Here, we have ...
1/3 = x^2/(1 -x^2) . . . . fill in given values for a, r, S
1 -x^2 = 3x^2 . . . . . cross multiply
1/4 = x^2
x = √(1/4)
x = ±1/2