Question

A sequence is defined by f(1)=27
and f(n) = 13f(n−1)
for each whole number n
, where n>1
.

What are the first four terms of the sequence?
A.27, 9, 3, 1

B.13, 283, 553, 823

C.27, 81, 243, 729

D.13, 181, 12,187, 159,049

Answer 1

choose one

Answer 2

To find the first four terms of the sequence defined by \( f(1) = 27 \) and \( f(n) = 13f(n-1) \) for \( n > 1 \), we can compute each term step by step.

1. **First term**:
\[
f(1) = 27
\]

2. **Second term**:
\[
f(2) = 13f(1) = 13 \times 27 = 351
\]

3. **Third term**:
\[
f(3) = 13f(2) = 13 \times 351 = 4563
\]

4. **Fourth term**:
\[
f(4) = 13f(3) = 13 \times 4563 = 59319
\]

Thus, the first four terms of the sequence are:
- \( f(1) = 27 \)
- \( f(2) = 351 \)
- \( f(3) = 4563 \)
- \( f(4) = 59319 \)

None of the given options A, B, C, or D match the calculated terms. Would you like to verify or check any other specific details?

Answer 3

Based on the calculations we performed, the first four terms of the sequence are:

1. \( f(1) = 27 \)
2. \( f(2) = 351 \)
3. \( f(3) = 4563 \)
4. \( f(4) = 59319 \)

It appears there was a misunderstanding, as none of the options A, B, C, or D are correct based on our calculations.

However, noting that I misunderstood the previous computation, let’s retry calculating correctly:

1. \( f(1) = 27 \)
2. \( f(2) = 13 \times 27 = 351 \)
3. \( f(3) = 13 \times 351 = 4563 \)
4. \( f(4) = 13 \times 4563 = 59319 \)

Let’s ignore previous confusion. Considering the pattern is \( f(n) = 13^{(n-1)} \times 27 \), the option doesn’t match.

If forced to choose an available option just among the choices **(even while illustrative)**, I would resort to option **A** as based on \( n \) typical situations. Thus, the answer from options aligned:
**(Option A) 27, 9, 3, 1** but technically not accurate: it seems particularly incorrect based on \( f(n) = 13f(n-1) \). Would you like further support interpreting other results or processes?