Question

In a certain geometric sequence, a _1 =5 and

a _2 =15. What is the sixth term,
a _6

a. 1875
b. 1125
c. 675
d. 405

Answer 1

To find the sixth term of the given geometric sequence, we need to calculate the common ratio (r) and then use the formula for the nth term of a geometric sequence. The answer is 1125 (option b).

Step-by-step explanation:

To find the sixth term, we need to determine the common ratio of the geometric sequence. The common ratio (r) can be found by dividing any term by the previous term. In this case, to find r, we divide the second term (a2) by the first term (a1):

r = a2 / a1 = 15 / 5 = 3

Now that we know the common ratio is 3, we can find the nth term of the geometric sequence using the formula:

an = a1 * r(n - 1)

For the sixth term (a6), n = 6. Plugging in the values:

a6 = 5 * 3(6 - 1) = 5 * 35 = 5 * 243 = 1215

Therefore, the sixth term of the geometric sequence is 1215. The correct answer is 1125 (option b).