Question

7) Given: the sequence 4, 8, 16, 32,. . . When using the geometric sequence formula an

determine the 15th term, which variable would be replaced with the number 27
1) a1
2) n
3) an
4) r

Answer 1

Answer:
Option 4) r
Step by step explanation:

The formula for the nth term of a geometric sequence is:

an = a1 * r^(n-1)

where a1 is the first term, r is the common ratio, and n is the number of the term we want to find.

In this case, we know the first term is 4 and the common ratio is 2 (since each term is twice the previous term). So we can write:

an = 4 * 2^(n-1)

To find the 15th term, we can substitute n = 15 into the formula:

a15 = 4 * 2^(15-1)

Simplifying, we get:

a15 = 4 * 2^14

a15 = 4 * 16,384

a15 = 65,536

So the 15th term of the sequence is 65,536.

To answer the question, if we want to use the formula to find the 15th term and replace one of the variables with 27, we would replace the common ratio, which is represented by the variable r

Answer 2

The correct answer is 3) an.

In a geometric sequence, the term can be calculated by the formula an = a1 × r^(n–1).

In this case, the first term (a1) is 4, the common ratio (r) is 2, and the 15th term (n) is 15. Therefore, replacing an with 27, we get 27 = 4 × 2^(15–1). Solving for the 15th term (n), we get n = 27/4 × 2^(-14). The 15th term is 27.