Question

Identify a1, r, and n for the sum of the geometric series. 1 2 3 8 9 32 27 128 81 512 a1 = r = n =

a) a1=1, r=2, n=10
b) a1=1, r=3, n=9
c) a1=1, r=4, n=8
d) a1=1, r=5, n=7

Answer 1

The given series is not a single geometric series but a combination of two. The correct values for a single geometric sequence cannot be determined from the given options, as no option correctly responds to the combined nature of the series provided.

Step-by-step explanation:

To identify a1, r, and n for the sum of the given geometric series, we need to establish the first term, the common ratio, and the number of terms. Looking at the sequence provided:

1. 1
2. 2
3. 3
4. 8
5. 9
6. 32
7. 27
8. 128
9. 81
10. 512

We can observe two separate sequences interwoven: one that starts with 1 and multiplies by 2 each time (1, 2, 4, 8, 16...) and another that starts with 3 and multiplies by 3 each time (3, 9, 27, 81...). Clearly, the two sequences are combined in an alternating fashion, and thus, we can't describe the entire series with a single geometric sequence formula.

Given the choices, none of them correctly represent the combined series as a geometric sequence. However, if we treat the question as though it is asking to identify a single sequence, option (a) is closest in fitting the part of the series that starts with 1 and has a common ratio of 2. But the question seems incorrectly framed for the provided series.