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Sum of Last N Terms Formula:
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The Sum of Last N Terms of a Geometric Progression calculates the total of the terms starting from the end to the nth term of a given geometric sequence. It provides the summation of terms in reverse order from the last term.
The calculator uses the formula:
Where:
Explanation: The formula calculates the sum of the last n terms by working backwards from the last term using the inverse of the common ratio.
Details: Calculating the sum of last n terms is crucial for various mathematical applications, including financial calculations, physics problems, and analyzing geometric sequences in reverse order.
Tips: Enter the last term of progression, common ratio (cannot be 0 or 1), and the number of terms from the end to sum. All values must be valid positive numbers.
Q1: Why can't the common ratio be 0 or 1?
A: A common ratio of 0 would make all terms zero (except possibly the first), and a ratio of 1 makes all terms equal, both leading to mathematical inconsistencies in the formula.
Q2: What if I want to sum terms from the beginning instead of the end?
A: Use the standard geometric series sum formula: \( S_n = a \times \frac{r^n - 1}{r - 1} \) for r ≠ 1.
Q3: Can this formula handle negative common ratios?
A: Yes, the formula works for negative common ratios, but the alternating signs may affect the sum result.
Q4: What are practical applications of this calculation?
A: Useful in finance for calculating reverse annuity payments, in physics for wave superposition, and in computer science for algorithm analysis.
Q5: How accurate is the calculator?
A: The calculator provides results with up to 6 decimal places precision, suitable for most mathematical and practical applications.