Which is the nth term of the sequence 5, 7, 11, 19, 35, …?
Answer and explanation
Correct answer: 2ⁿ + 3
The terms follow a doubling pattern with a fixed addition. They can be rewritten as 5 = 2¹ + 3, 7 = 2² + 3, 11 = 2³ + 3, 19 = 2⁴ + 3, and 35 = 2⁵ + 3. Therefore, when the first term is indexed by n = 1, the general term is aₙ = 2ⁿ + 3. Option A is correct. Substitution verifies every listed term, not merely the first one. Option B gives 5 for n = 1 but gives 9 for n = 2, so its exponent or constant is unsuitable. Option C produces 5, 6, 11, 19, 35 only inconsistently, and option D is linear, with constant first differences, unlike this sequence.
Frequently asked questions
What is the correct answer to this question?
2ⁿ + 3
Why is this the correct answer?
The terms follow a doubling pattern with a fixed addition. They can be rewritten as 5 = 2¹ + 3, 7 = 2² + 3, 11 = 2³ + 3, 19 = 2⁴ + 3, and 35 = 2⁵ + 3. Therefore, when the first term is indexed by n = 1, the general term is aₙ = 2ⁿ + 3. Option A is correct. Substitution verifies every listed term, not merely the first one. Option B gives 5 for n = 1 but gives 9 for n = 2, so its exponent or constant is unsuitable. Option C produces 5, 6, 11, 19, 35 only inconsistently, and option D is linear, with constant first differences, unlike this sequence.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
