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?

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

To solve the problem, we need to determine the fourth term in a sequence where each term is obtained by multiplying the previous term by 2 and then subtracting 1, starting from the first term which is 3.

1. Understanding the Situation: 
- First term (T₁) = 3
- Recursive relation: Tₙ = 2 × Tₙ₋₁ − 1
- We are required to find the fourth term (T₄) of the sequence.

Key Concept: We apply the given recurrence relation repeatedly to compute the next terms based on the previous ones.

2. Generating the Terms: 
- T₁ = 3 (given)
- T₂ = 2 × T₁ − 1 = 2 × 3 − 1 = 6 − 1 = 5
- T₃ = 2 × T₂ − 1 = 2 × 5 − 1 = 10 − 1 = 9
- T₄ = 2 × T₃ − 1 = 2 × 9 − 1 = 18 − 1 = 17

Final Answer: 
The fourth term in the sequence is 17.