What is the 7th term of the sequence 4, 20, 100, 500, …?
Answer and explanation
Correct answer: 62,500
The governing concept is the general term of a geometric progression. Each term is obtained by multiplying the previous term by 5, so the first term is a₁ = 4 and the common ratio is r = 5. The nth-term formula is aₙ = arⁿ⁻¹. Therefore a₇ = 4 × 5⁶. Since 5⁶ = 15,625, the product is 4 × 15,625 = 62,500. Equivalently, continuing gives a₆ = 15,625 and a₇ = 78,125? This reveals the listed sequence indexing check: 4,20,100,500 gives a₅=2500, a₆=12500, a₇=62500. Thus option C is correct. The apparent intermediate alternative 15,625 is a₆ only under a mistaken count.
Frequently asked questions
What is the correct answer to this question?
62,500
Why is this the correct answer?
The governing concept is the general term of a geometric progression. Each term is obtained by multiplying the previous term by 5, so the first term is a₁ = 4 and the common ratio is r = 5. The nth-term formula is aₙ = arⁿ⁻¹. Therefore a₇ = 4 × 5⁶. Since 5⁶ = 15,625, the product is 4 × 15,625 = 62,500. Equivalently, continuing gives a₆ = 15,625 and a₇ = 78,125? This reveals the listed sequence indexing check: 4,20,100,500 gives a₅=2500, a₆=12500, a₇=62500. Thus option C is correct. The apparent intermediate alternative 15,625 is a₆ only under a mistaken count.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
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