हिन्दी में पढ़ेंHome › Formulas › Geometric & harmonic progressions › GP sum
GP sum
Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1
Where: Sₙ = sum of n terms, a = first term / coefficient a, n = number of terms, r = common ratio
Solved example
Given: a = 7, n = 5, r = 10
Find: S_n (sum of n terms)
- Formula: Sₙ = a·(r^n - 1)/(r - 1)
- Substitute the values: Sₙ = 7·(10^5 - 1)/(10 - 1)
- Result: Sₙ = 77777
Answer: S_n = 77777
Calculator
How to calculate GP sum
- Write down the formula: Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1.
- Note the known values (a, n, r).
- Substitute them and simplify to find S_n.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for GP sum?
The formula is Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1, where Sₙ = sum of n terms, a = first term / coefficient a, n = number of terms, r = common ratio.
What is GP sum when a = 7, n = 5, r = 10?
S_n = 77777. Substitute the values into Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1 and simplify.