Which explicit rule is correct for the sequence 2, 11/2, 21/2, 17, …?
Answer and explanation
Correct answer: aₙ = (3n² + 5n)/4
The governing idea is verification of an explicit general term by substituting successive values of n. For option A, n = 1 gives (3 + 5)/4 = 2. For n = 2, (3·4 + 10)/4 = 22/4 = 11/2. For n = 3, (3·9 + 15)/4 = 42/4 = 21/2. For n = 4, (3·16 + 20)/4 = 68/4 = 17. Thus A reproduces all four terms exactly. Option B gives 2, 5 and 9, option C gives 2, 5 and 8, and option D gives 3/2 for the first term. Consequently, fractional terms must be checked carefully rather than rounded or treated as whole numbers.
Frequently asked questions
What is the correct answer to this question?
aₙ = (3n² + 5n)/4
Why is this the correct answer?
The governing idea is verification of an explicit general term by substituting successive values of n. For option A, n = 1 gives (3 + 5)/4 = 2. For n = 2, (3·4 + 10)/4 = 22/4 = 11/2. For n = 3, (3·9 + 15)/4 = 42/4 = 21/2. For n = 4, (3·16 + 20)/4 = 68/4 = 17. Thus A reproduces all four terms exactly. Option B gives 2, 5 and 9, option C gives 2, 5 and 8, and option D gives 3/2 for the first term. Consequently, fractional terms must be checked carefully rather than rounded or treated as whole numbers.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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