What is the sixth term of the sequence 6, 30, 150, 750, …?
Answer and explanation
Correct answer: 18750
This is a geometric progression because each term is obtained by multiplying the preceding term by 5: 30/6 = 5, 150/30 = 5, and 750/150 = 5. For a geometric sequence, aₙ = arⁿ⁻¹, where a is the first term and r is the common ratio. Here a = 6 and r = 5, so a₆ = 6 × 5⁵. Since 5⁵ = 3125, a₆ = 6 × 3125 = 18750. Thus option A is correct. The exponent is 5 rather than 6 because the first term already contains the initial factor. Options C and D use an insufficient or incorrect multiplication, while option B does not follow the progression.
Frequently asked questions
What is the correct answer to this question?
18750
Why is this the correct answer?
This is a geometric progression because each term is obtained by multiplying the preceding term by 5: 30/6 = 5, 150/30 = 5, and 750/150 = 5. For a geometric sequence, aₙ = arⁿ⁻¹, where a is the first term and r is the common ratio. Here a = 6 and r = 5, so a₆ = 6 × 5⁵. Since 5⁵ = 3125, a₆ = 6 × 3125 = 18750. Thus option A is correct. The exponent is 5 rather than 6 because the first term already contains the initial factor. Options C and D use an insufficient or incorrect multiplication, while option B does not follow the progression.
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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