What is the general term of the sequence 3, 21, 119, 617, ...?
Answer and explanation
Correct answer: a_n = 5^n - 2n
The governing concept is verifying a proposed explicit general term by substituting successive positive integers. For option A, n = 1 gives 5 − 2 = 3; n = 2 gives 25 − 4 = 21; n = 3 gives 125 − 6 = 119; and n = 4 gives 625 − 8 = 617. Every displayed term is reproduced, so a_n = 5^n − 2n is correct. Option B grows only linearly, option C gives 3, 5, 9, 17, and option D gives negative values initially or does not match the sequence. Checking several indices prevents accepting a formula that fits only one term.
Frequently asked questions
What is the correct answer to this question?
a_n = 5^n - 2n
Why is this the correct answer?
The governing concept is verifying a proposed explicit general term by substituting successive positive integers. For option A, n = 1 gives 5 − 2 = 3; n = 2 gives 25 − 4 = 21; n = 3 gives 125 − 6 = 119; and n = 4 gives 625 − 8 = 617. Every displayed term is reproduced, so a_n = 5^n − 2n is correct. Option B grows only linearly, option C gives 3, 5, 9, 17, and option D gives negative values initially or does not match the sequence. Checking several indices prevents accepting a formula that fits only one term.
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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