What is the first term in the geometric progression (12, 36, 108, 324, ...)?
Answer and explanation
Correct answer: 12
The governing concept is the identification of the first term of a geometric progression. In a GP, the first term is denoted by a, and every later term is obtained by multiplying the preceding term by a fixed common ratio r. The displayed order is important: the first number written is the first term. Here the sequence starts with 12, so a = 12. The common ratio confirms the pattern because 36 ÷ 12 = 3, 108 ÷ 36 = 3, and 324 ÷ 108 = 3. Thus 3 is the common ratio, not the first term; 36 and 108 are later terms. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The governing concept is the identification of the first term of a geometric progression. In a GP, the first term is denoted by a, and every later term is obtained by multiplying the preceding term by a fixed common ratio r. The displayed order is important: the first number written is the first term. Here the sequence starts with 12, so a = 12. The common ratio confirms the pattern because 36 ÷ 12 = 3, 108 ÷ 36 = 3, and 324 ÷ 108 = 3. Thus 3 is the common ratio, not the first term; 36 and 108 are later terms. Therefore, option B is correct.
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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