What is the 8th term of the sequence 3, 9, 27, 81, …?
Answer and explanation
Correct answer: 6561
The governing concept is the nth term of a geometric progression, aₙ = arⁿ⁻¹. Here the first term is a = 3 and the common ratio is r = 9/3 = 3. Therefore the eighth term is a₈ = 3 × 3⁷ = 3⁸. Evaluating the power gives 3⁸ = 6561. Hence option C, not option A, is correct. Option A, 2187, equals 3⁷ and results from using one fewer multiplication. Option B is 3⁶, while option D is 3⁵. The term number matters because the first term already contains one factor of 3, so the eighth term contains eight factors in total.
Frequently asked questions
What is the correct answer to this question?
6561
Why is this the correct answer?
The governing concept is the nth term of a geometric progression, aₙ = arⁿ⁻¹. Here the first term is a = 3 and the common ratio is r = 9/3 = 3. Therefore the eighth term is a₈ = 3 × 3⁷ = 3⁸. Evaluating the power gives 3⁸ = 6561. Hence option C, not option A, is correct. Option A, 2187, equals 3⁷ and results from using one fewer multiplication. Option B is 3⁶, while option D is 3⁵. The term number matters because the first term already contains one factor of 3, so the eighth term contains eight factors in total.
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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