What is the nth term of the sequence 13, 29, 61, 125, 253, …?
Answer and explanation
Correct answer: 2ⁿ⁺³ − 3
The governing idea is to express each term using the same power pattern. The sequence can be rewritten as 13 = 16 − 3, 29 = 32 − 3, 61 = 64 − 3, 125 = 128 − 3, and 253 = 256 − 3. These powers are 2⁴, 2⁵, 2⁶, 2⁷, and 2⁸, so the power in the nth term is 2ⁿ⁺³. Hence aₙ = 2ⁿ⁺³ − 3. For n = 1, this gives 16 − 3 = 13, and for n = 5 it gives 256 − 3 = 253. Option A gives the wrong exponent and constant, option C does not fit the first term, and option D is linear rather than exponential.
Frequently asked questions
What is the correct answer to this question?
2ⁿ⁺³ − 3
Why is this the correct answer?
The governing idea is to express each term using the same power pattern. The sequence can be rewritten as 13 = 16 − 3, 29 = 32 − 3, 61 = 64 − 3, 125 = 128 − 3, and 253 = 256 − 3. These powers are 2⁴, 2⁵, 2⁶, 2⁷, and 2⁸, so the power in the nth term is 2ⁿ⁺³. Hence aₙ = 2ⁿ⁺³ − 3. For n = 1, this gives 16 − 3 = 13, and for n = 5 it gives 256 − 3 = 253. Option A gives the wrong exponent and constant, option C does not fit the first term, and option D is linear rather than exponential.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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