Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the given geometric sequence. *16,32,64,128,....* Given that the sequence is represented by the function f, complete the statements. The common ratio is . f(1) = f(5) =

Answer 1

The common ratio in the given geometric sequence is 2. f(1) = 16 and f(5) = 256.

Step-by-step explanation:

The common ratio in the given geometric sequence is 2. This can be determined by dividing each term by the term before it. For example, 32 ÷ 16 = 2. Therefore, the common ratio is 2.

To find f(1), we substitute 1 into the function f. Since the first term in the sequence is 16, f(1) = 16.

To find f(5), we need to find the fifth term in the sequence. Using the formula for a geometric sequence, aₙ = a₁ * r^(n-1), where aₙ is the nth term, a₁ is the first term, r is the common ratio, and n is the position of the term, we can plug in the values: a₅ = 16 * 2^(5-1) = 16 * 2^4 = 16 * 16 = 256. Therefore, f(5) = 256.