Geometric Progression — Important Questions
Gujarat Board · Class 11 · Statistics
45 important questions from Geometric Progression for Gujarat Board Class 11 Statistics, with answers. Includes multiple choice and multiple correct.
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Important Questions from Geometric Progression
Which of the following are geometric progressions?
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1, 3, 9, 27, ..., 5, 10, 20, 40, ..., 8, 4, 2, 1, ...
A GP has constant ratio between consecutive terms. (1,3,9,27) has ratio 3, (5,10,20,40) has ratio 2, (8,4,2,1) has ratio 1/2. The others are arithmetic progressions.
If the first term of a GP is 4 and the common ratio is 1/2, what is the third term?
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1
Using Tn = ar^(n-1), T3 = 4 × (1/2)^(3-1) = 4 × (1/2)^2 = 4 × 1/4 = 1.
What is the sum formula for first n terms of a GP when r ≠ 1?
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Sn = a(r^n - 1)/(r - 1)
For a GP with r ≠ 1, the sum of first n terms is Sn = a(r^n - 1)/(r - 1), where a is the first term and r is the common ratio.
Find the sum of first 4 terms of GP: 2, 6, 18, 54, ...
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80
a = 2, r = 3, n = 4. Using Sn = a(r^n - 1)/(r - 1): S4 = 2(3^4 - 1)/(3 - 1) = 2(81 - 1)/2 = 2 × 40 = 80.
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