If aₙ = 64 × (1/2)ⁿ⁻¹, what is the value of a₅?
Answer and explanation
Correct answer: 4
This question uses an explicit or general rule for a geometric progression. To find the fifth term, substitute n = 5 into aₙ = 64 × (1/2)ⁿ⁻¹. Thus a₅ = 64 × (1/2)⁵⁻¹ = 64 × (1/2)⁴. Since (1/2)⁴ = 1/16, a₅ = 64 × 1/16 = 4. Therefore option B is correct. The exponent is n − 1 because the first term contains zero factors of the common ratio; the fifth term contains four. Using exponent 5 would give 2, which explains option A but violates the stated formula. Three factors give 8, and one factor gives 32, neither of which is a₅.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
This question uses an explicit or general rule for a geometric progression. To find the fifth term, substitute n = 5 into aₙ = 64 × (1/2)ⁿ⁻¹. Thus a₅ = 64 × (1/2)⁵⁻¹ = 64 × (1/2)⁴. Since (1/2)⁴ = 1/16, a₅ = 64 × 1/16 = 4. Therefore option B is correct. The exponent is n − 1 because the first term contains zero factors of the common ratio; the fifth term contains four. Using exponent 5 would give 2, which explains option A but violates the stated formula. Three factors give 8, and one factor gives 32, neither of which is a₅.
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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