Which is the nth term of the sequence 4, 10, 18, 28, 40, …?
Answer and explanation
Correct answer: n² + 3n
The governing concept is identifying an explicit rule by testing the index values. For option C, put n = 1: 1² + 3(1) = 4; n = 2 gives 4 + 6 = 10; n = 3 gives 9 + 9 = 18; n = 4 gives 16 + 12 = 28; and n = 5 gives 25 + 15 = 40. Thus every displayed term is reproduced by aₙ = n² + 3n. The other options fail immediately: option A gives 3 for n = 1, option B gives 4 but then 10 for n = 2? Actually it gives 10 at n = 2 but fails at n = 3, and option D gives 5 for n = 1. Hence option C is the only rule matching the sequence.
Frequently asked questions
What is the correct answer to this question?
n² + 3n
Why is this the correct answer?
The governing concept is identifying an explicit rule by testing the index values. For option C, put n = 1: 1² + 3(1) = 4; n = 2 gives 4 + 6 = 10; n = 3 gives 9 + 9 = 18; n = 4 gives 16 + 12 = 28; and n = 5 gives 25 + 15 = 40. Thus every displayed term is reproduced by aₙ = n² + 3n. The other options fail immediately: option A gives 3 for n = 1, option B gives 4 but then 10 for n = 2? Actually it gives 10 at n = 2 but fails at n = 3, and option D gives 5 for n = 1. Hence option C is the only rule matching the sequence.
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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