Question

The formula for any geometric sequence is an = a1 · rn - 1 , where an represents the value of the n th term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the geometric sequence 4, 8, 16, 32, ...?

A. an = 4 · (1/2) n - 1
B. an = 2 · 4 n - 1
C. an = 32 · 2 n - 1
D. an = 4 · 2 n - 1

Answer 1

Answer: The correct answer would be

D. an = 4.2n-1

Step-by-step explanation: First, calculate the ratios between each term and the one that precedes it.

8/4=2 ....16/8=2...32/16= 2...

Upon comparing the ratios we see the ratio between each term and the one that precedes it is 2 for all the terms, the sequence is geometric, and the common ratio is r = 2.

Now, we simply need to find the other unknown values in the equation, a1= the first term of the sequence which is 4, Therefore a1=4

Looking at the options provided we see that no further missing quantity can further be found so we put this in the equation provided for a geometric sequence.

We get 4. 2n-1, which is our answer.