98.3k views
2 votes
Find the sum of the 2 terms of a generic sequence where the first term the common ratio - 1/2

1 Answer

0 votes

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.

User JRichardsz
by
7.7k points