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 solve the problem, we need to apply the rule of the sequence repeatedly starting from the first term to find the fourth term.

1. Understanding the Concepts:

- Sequence Rule: Each term is generated by multiplying the previous term by 2 and then subtracting 1.
- Recursive Formula: \( a_n = 2 \times a_{n-1} - 1 \), where \( a_1 = 3 \)
- Goal: Find the value of the 4th term \( a_4 \)

2. Given Values:

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

3. Calculating the Terms:

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

Final Answer:

The fourth term in the sequence is 17.