Question

In the sequence F, the first term has the value seven, and each successive term is obtained by μltiplying the previous term by the constant r. What is the value of r?

a. The value of the fourteenth term of sequence F is sixteen × the value of the twelfth term.
b. Insufficient information to determine the value of r.
c. The value of r is 16.
d. None of the above.

Answer 1

To find the value of r in the sequence, we can use the information given in the question and equation. The correct value of r is 16^(1/13).

Step-by-step explanation:

To find the value of r, we need to examine the information given in the question. We are told that the first term of the sequence is 7, and each successive term is obtained by multiplying the previous term by a constant r. In option a, it states that the fourteenth term is sixteen times the twelfth term. We can use this information to find the value of r. Let's set up an equation:

4th term = 1st term * (r^3) = 7 * r^3

14th term = 1st term * (r^13) = 7 * r^13

From option a, we know that 14th term = 16 * 12th term. Plugging in the values, we get:

7 * r^13 = 16 * 7 * r^9

Cancelling out the 7s, we have:

r^13 = 16 * r^9

Raising both sides of the equation to the power of 1/9, we get:

r^(13/9) = 16^(1/9)

Simplifying further, we find:

r = 16^(1/13)

Therefore, the value of r is 16^(1/13). The correct answer is None of the above (d).