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

The objective is to determine the fourth term of a sequence. The sequence commences with 3, and each subsequent term is generated by multiplying the preceding term by 2 and then subtracting 1.

1. Problem Definition:
- Initial term (T₁) = 3
- Rule for generating terms: Tₙ = 2 × Tₙ₋₁ − 1
- Target: Find the fourth term (T₄).

Methodology: The recursive relation will be applied sequentially to calculate each term.

2. Term Calculation: 
- T₁ = 3 (given)
- T₂ = (2 × 3) − 1 = 5
- T₃ = (2 × 5) − 1 = 9
- T₄ = (2 × 9) − 1 = 17

Conclusion: 
The fourth term of the sequence is 17.