If a = 4 and r = 5, what is the third term of the geometric progression?
Answer and explanation
Correct answer: 100
The governing concept is the nth-term rule for a geometric progression: aₙ = arⁿ⁻¹, where a is the first term and r is the common ratio. For the third term, n = 3, so the exponent is 3 − 1 = 2. Hence a₃ = 4 × 5² = 4 × 25 = 100. The same result appears by generating the terms: the first term is 4, the second is 4 × 5 = 20, and the third is 20 × 5 = 100. Therefore, option C is correct. Option A does not result from two multiplications by 5, option B comes from an incorrect calculation, and option D treats the expression as 5³ instead of 4 × 5².
Frequently asked questions
What is the correct answer to this question?
100
Why is this the correct answer?
The governing concept is the nth-term rule for a geometric progression: aₙ = arⁿ⁻¹, where a is the first term and r is the common ratio. For the third term, n = 3, so the exponent is 3 − 1 = 2. Hence a₃ = 4 × 5² = 4 × 25 = 100. The same result appears by generating the terms: the first term is 4, the second is 4 × 5 = 20, and the third is 20 × 5 = 100. Therefore, option C is correct. Option A does not result from two multiplications by 5, option B comes from an incorrect calculation, and option D treats the expression as 5³ instead of 4 × 5².
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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