What is the tenth term of the geometric progression (2, 6, 18, 54, ...)?
Answer and explanation
Correct answer: 39366
The governing concept is the nth-term formula for a geometric progression: aₙ = arⁿ⁻¹. In the given sequence, the first term is a = 2 and the common ratio is r = 6 ÷ 2 = 3; the same ratio continues because 18 ÷ 6 and 54 ÷ 18 are also 3. For the tenth term, substitute n = 10: a₁₀ = 2 × 3⁹. Since 3⁹ = 19683, the result is 2 × 19683 = 39366. Therefore option B is correct. Option A is only 3⁹ and omits the first-term factor 2; option C corresponds to 3¹⁰, while option D doubles the correct value again. The exponent is n − 1 because the first term has zero ratio multiplications.
Frequently asked questions
What is the correct answer to this question?
39366
Why is this the correct answer?
The governing concept is the nth-term formula for a geometric progression: aₙ = arⁿ⁻¹. In the given sequence, the first term is a = 2 and the common ratio is r = 6 ÷ 2 = 3; the same ratio continues because 18 ÷ 6 and 54 ÷ 18 are also 3. For the tenth term, substitute n = 10: a₁₀ = 2 × 3⁹. Since 3⁹ = 19683, the result is 2 × 19683 = 39366. Therefore option B is correct. Option A is only 3⁹ and omits the first-term factor 2; option C corresponds to 3¹⁰, while option D doubles the correct value again. The exponent is n − 1 because the first term has zero ratio multiplications.
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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