What is the first term in the geometric progression (9, 27, 81, 243, ...)?
Answer and explanation
Correct answer: 9
In a geometric progression, the first term is simply the first number written in the ordered sequence. The common ratio and later terms are useful for describing the pattern, but they do not change the identity of the first term. In the sequence (9,27,81,243,dots), the sequence begins with 9.
Thus a=9, and option B is correct. The pattern also confirms this: each term is obtained by multiplying the previous term by 3, since 27/9=3 and 81/27=3. However, this calculation is not needed to identify the first term. The displayed alternatives use fractions such as 9/9, but the intended listed value is the initial term 9, not a ratio or a quotient.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
In a geometric progression, the first term is simply the first number written in the ordered sequence. The common ratio and later terms are useful for describing the pattern, but they do not change the identity of the first term. In the sequence (9,27,81,243,dots), the sequence begins with 9.
Thus a=9, and option B is correct. The pattern also confirms this: each term is obtained by multiplying the previous term by 3, since 27/9=3 and 81/27=3. However, this calculation is not needed to identify the first term. The displayed alternatives use fractions such as 9/9, but the intended listed value is the initial term 9, not a ratio or a quotient.
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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