Thanks. The formula is first term*(1-r^n)/(1-r). How does 1-r become reversed in the solution?andrewkirk said:
A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a constant factor. For example, the series 1, 2, 4, 8, 16, 32... is a geometric series with a common ratio of 2.
To find the sum of a geometric series, you can use the formula S = a(1-r^n)/(1-r), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms in the series. Alternatively, you can also use the formula S = a/(1-r), where S is the sum, a is the first term, and r is the common ratio, if the number of terms goes to infinity.
A finite geometric series has a fixed number of terms, while an infinite geometric series continues on forever. In a finite series, the sum can be calculated using the formula S = a(1-r^n)/(1-r) where n is the number of terms. In an infinite series, the sum can be calculated using the formula S = a/(1-r), where a is the first term and r is the common ratio.
Yes, a geometric series can have a negative common ratio. This means that the series will alternate between positive and negative numbers. For example, the series 1, -2, 4, -8, 16... is a geometric series with a common ratio of -2.
Geometric series can be used to model real-life situations such as population growth, compound interest, and depreciation. For example, a population that doubles every year can be represented by a geometric series with a common ratio of 2. This can also be applied to investments with compound interest, where the principal amount grows exponentially over time.