Geometric sequence calculator
A geometric sequence multiplies by a constant each step. If that constant is under one in size, the infinite sum converges.
nth term
39 366
- Sum of the first n terms
- 59 048
- Sum to infinity Only defined when the ratio is between -1 and 1.
- 0
- Converges
- 0
Show the working
- First term = 2
- Common ratio = 3
- Number of terms = 10
- nth term = 2 * 3^(10 - 1) = 39 366
- Sum of the first n terms = 3 == 1 ? 2 * 10 : 2 * (3^10 - 1) / (3 - 1) = 59 048
- Converges = abs(3) < 1 ? 1 : 0 = 0
- Sum to infinity = abs(3) < 1 ? 2 / (1 - 3) : 0 = 0
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- a(n) = a1 r^(n-1)
- S(n) = a1 (r^n - 1) / (r - 1)
- S(infinity) = a1 / (1 - r) when |r| < 1