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Important Formulas: Geometric Progression-1 Video Lecture | CSAT Preparation - UPSC

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FAQs on Important Formulas: Geometric Progression-1 Video Lecture - CSAT Preparation - UPSC

1. What is a geometric progression?
Ans. Geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
2. How do you find the nth term of a geometric progression?
Ans. The formula to find the nth term of a geometric progression is given by \( a_n = a_1 \times r^{(n-1)} \), where \( a_n \) is the nth term, \( a_1 \) is the first term, r is the common ratio, and n is the position of the term.
3. What is the sum of n terms in a geometric progression?
Ans. The sum of n terms in a geometric progression can be calculated using the formula \( S_n = \frac{a_1(r^n - 1)}{r-1} \), where \( S_n \) is the sum of n terms, \( a_1 \) is the first term, r is the common ratio, and n is the number of terms.
4. How do you determine if a sequence is a geometric progression?
Ans. A sequence is considered a geometric progression if the ratio of any term to the previous term is constant. In other words, if \( \frac{a_{n+1}}{a_n} \) is the same for all n, then the sequence is a geometric progression.
5. How can geometric progression be applied in real-life situations?
Ans. Geometric progression can be used in various real-life scenarios such as population growth, interest calculations, and exponential decay. It helps in predicting future values based on a constant rate of change.
214 videos|139 docs|151 tests

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