 |  Geometric Progression 30 Flashcards |  Start |
 | What is the formula for the nth term of a geometric progression? |  Card: 1 / 30 |
| The formula for the nth term of a geometric progression is tₙ = a × r^(n-1), where a is the first term and r is the common ratio. | Card: 2 / 30 |
| If the first term of a geometric progression is 5 and the common ratio is 3, what is the 4th term? | Card: 3 / 30 |
|  The 4th term t₄ = 5 × 3^(4-1) = 5 × 27 = 135. | Card: 4 / 30 |
| True or False: The sum of an infinite geometric series exists only if the common ratio is greater than 1. | Card: 5 / 30 |
|  False. The sum exists if the absolute value of the common ratio is less than 1. | Card: 6 / 30 |
| Fill in the blank: The geometric mean G between two numbers a and b is calculated as G = ___(a × b). | Card: 7 / 30 |
|  √ | Card: 8 / 30 |
| What is the sum of the first 5 terms of a geometric progression with first term 10 and common ratio 2? | Card: 9 / 30 |
|  The sum S₅ = 10 × (2⁵ - 1) / (2 - 1) = 10 × (32 - 1) = 10 × 31 = 310. | Card: 10 / 30 |
| If the 3rd term of a geometric progression is 16 and the common ratio is 2, what is the first term? | Card: 11 / 30 |
|  The first term a = 16 / 2² = 16 / 4 = 4. | Card: 12 / 30 |
| True or False: If a sequence is a geometric progression, the ratio of consecutive terms must be constant. | Card: 13 / 30 |
|  True. | Card: 14 / 30 |
| Find the sum of the first 6 terms of the geometric series 1, 3, 9, 27,... | Card: 15 / 30 |
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|  The sum S₆ = 1 × (3⁶ - 1) / (3 - 1) = 1 × (729 - 1) / 2 = 728 / 2 = 364. | Card: 16 / 30 |
| If the first term of a geometric progression is 8 and the 5th term is 1, what is the common ratio? | Card: 17 / 30 |
|  Let r be the common ratio. Then, 8 × r⁴ = 1, so r⁴ = 1/8, thus r = 1/2. | Card: 18 / 30 |
| Fill in the blank: The general form of the sum of the first n terms when the common ratio is less than 1 is Sₙ = a × (1 - rⁿ) / (1 - r). | Card: 19 / 30 |
|  True. | Card: 20 / 30 |
| What is the 7th term of the geometric sequence where the first term is 4 and the common ratio is 3? | Card: 21 / 30 |
|  The 7th term t₇ = 4 × 3^(7-1) = 4 × 729 = 2916. | Card: 22 / 30 |
| Which of the following statements is true regarding the properties of geometric progressions? | Card: 23 / 30 |
| Multiplying terms retains properties.
| Card: 24 / 30 |
| Calculate the 10th term of the geometric progression where the first term is 2 and the common ratio is 5. | Card: 25 / 30 |
|  The 10th term t₁₀ = 2 × 5^(10-1) = 2 × 5⁹ = 2 × 1953125 = 3906250. | Card: 26 / 30 |
| True or False: The product of the first five terms of a geometric progression is equal to the square of the 3rd term multiplied by the 4th term. | Card: 27 / 30 |
|  True. | Card: 28 / 30 |
| The nth term of a geometric progression can be expressed as tn = ___ × ___ⁿ⁻¹. | Card: 29 / 30 |
|  A, r | Card: 30 / 30 |
| Completed! Keep practicing to master all of them. |  Restart |
