If a geometric progression has first term 5 and common ratio 3, what is the second term?
Answer and explanation
Correct answer: 15
The governing property of a geometric progression is multiplicative: every term after the first is obtained by multiplying the preceding term by the common ratio. Here a₁ = 5 and r = 3, so a₂ = a₁r = 5 × 3 = 15. Therefore, option D is correct. Option A comes from adding 3 to 5, which is the type of operation associated with an arithmetic progression, not a geometric one. Option B would result from multiplying by 2, and option C does not use the stated ratio in any valid way. The defining operation is multiplication by 3, so the sequence would begin 5, 15, 45, 135, and so on. This confirms that 15 is the only suitable answer.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The governing property of a geometric progression is multiplicative: every term after the first is obtained by multiplying the preceding term by the common ratio. Here a₁ = 5 and r = 3, so a₂ = a₁r = 5 × 3 = 15. Therefore, option D is correct. Option A comes from adding 3 to 5, which is the type of operation associated with an arithmetic progression, not a geometric one. Option B would result from multiplying by 2, and option C does not use the stated ratio in any valid way. The defining operation is multiplication by 3, so the sequence would begin 5, 15, 45, 135, and so on. This confirms that 15 is the only suitable answer.
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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