Question

For a geometric sequence, find the sum of the first 5 terms if a 1=4 and r=2. Select one:

a. 68
b. 124
c. 231
d. 78

Answer 1

The sum of the first 5 terms of the geometric sequence with a first term of 4 and a common ratio of 2 is 124.

Step-by-step explanation:

A geometric sequence is a sequence in which each term is found by multiplying the previous term by a constant number called the common ratio (r).

In this case, the first term (a1) is 4 and the common ratio (r) is 2.

To find the sum of the first 5 terms of a geometric sequence, we can use the formula: Sn = a1(1 - rn)/(1 - r), where Sn is the sum of the first n terms.

Substituting the values into the formula, we get: S5 = 4(1 - 25)/(1 - 2).

Simplifying the expression, we find that the sum of the first 5 terms is 4(-31)/(-1) = 124.