Final answer:
The sum of the terms in a geometric sequence can be found using the formula: S = a(1 - r^n)/(1 - r), where a is the first term, r is the common ratio, and n is the number of terms.
Step-by-step explanation:
The sum of a geometric sequence can be found using the formula:
S = a(1 - r^n)/(1 - r)
where:
- S is the sum of the sequence
- a is the first term
- r is the common ratio
- n is the number of terms
In this case, the first term is -1/2 and the common ratio is 1/2. We can substitute these values into the formula:
S = -1/2(1 - (1/2)^n)/(1 - 1/2)
Simplifying further:
S = -1/2(2 - (1/2)^n)
So the sum of the sequence is -1/2(2 - (1/2)^n).
The question is about finding the sum of the first two terms of a geometric sequence where the first term is not given, but the common ratio is -1/2. If we denote the first term of the sequence as a, the second term would be a × (-1/2). The sum of these two terms is a + a × (-1/2) = a - a/2 = a/2.
Without the value of the first term a, we cannot provide a numerical answer, but we have the expression for the sum of the first two terms of the sequence.