If (a=3) and (r=4), what is the third term of the geometric progression?
Answer and explanation
Correct answer: (48)
In a geometric progression, each term is obtained by multiplying the preceding term by the same common ratio r. If the first term is a, the terms begin as a, ar, and then \(ar^2\). Therefore the third term is found using the ratio twice, not once. With a=3 and r=4, the third term is \(ar^2=3\times4^2=3\times16=48\).
The sequence can also be written step by step: the first term is 3, the second is \(3\times4=12\), and the third is \(12\times4=48\). Hence option C is correct. The value 12 is the second term, while 24 does not follow the required multiplication pattern. The value 64 is only \(4^3\), so it ignores the first term 3. The exponent in the formula is one less than the term number.
Frequently asked questions
What is the correct answer to this question?
(48)
Why is this the correct answer?
In a geometric progression, each term is obtained by multiplying the preceding term by the same common ratio r. If the first term is a, the terms begin as a, ar, and then \(ar^2\). Therefore the third term is found using the ratio twice, not once. With a=3 and r=4, the third term is \(ar^2=3\times4^2=3\times16=48\).
The sequence can also be written step by step: the first term is 3, the second is \(3\times4=12\), and the third is \(12\times4=48\). Hence option C is correct. The value 12 is the second term, while 24 does not follow the required multiplication pattern. The value 64 is only \(4^3\), so it ignores the first term 3. The exponent in the formula is one less than the term number.
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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