Question

In a sequence of numbers, each term is generated by multiplying the previous term by 2 and then subtracting 1. If the first term is 3, what is the fourth term in the sequence?

• A. 11
• B. 17
• C. 23
• D. 25

Hint:

Remember: In sequence questions, carefully apply the given rule to each term. If the answer doesn’t match options, double-check the pattern or term number requested.

Answer 1

The Correct Option is B

To determine the fourth term, we will apply the established sequence rule iteratively, commencing with the initial term.

1. Foundational Principles:

- Sequence Operational Rule: Each subsequent term is derived by doubling the preceding term and subsequently subtracting one.
- Iterative Definition: \( a_n = 2 \times a_{n-1} - 1 \), with \( a_1 = 3 \)
- Objective: Ascertain the value of the 4th term, denoted as \( a_4 \)

2. Provided Data:

Initial term \( a_1 = 3 \)
Iterative rule: \( a_n = 2 \times a_{n-1} - 1 \)

3. Term Computation:

\[a_2 = 2 \times a_1 - 1 = 2 \times 3 - 1 = 6 - 1 = 5\]
\[a_3 = 2 \times a_2 - 1 = 2 \times 5 - 1 = 10 - 1 = 9\]
\[a_4 = 2 \times a_3 - 1 = 2 \times 9 - 1 = 18 - 1 = 17\]

Conclusive Result:

The resultant value for the fourth term in the sequence is 17.