š¢ Discrete Mathematics & Infinite Series
Arithmetic & Geometric Sequence Calculator
Compute the $n^{\text{th}}$ term ($a_n$), partial sum ($S_n$), common step difference ($d$) or ratio ($r$), and evaluate infinite geometric series convergence ($S_\infty$).
Sequence Parameters
10th Term (aāā)
39.00
Sum ($S_n$)
210.00
Infinite Sum ($S_\infty$)
Divergent (AP)
First 5 Terms
3, 7, 11, 15, 19
š” Explicit Formula:
$$a_n = 3 + (n - 1) \times 4 = 4n - 1 \implies a_{10} = 39$$
Arithmetic & Geometric Formulas
Arithmetic Progression (AP)
- $n^{\text{th}}$ Term: $$a_n = a_1 + (n-1)d$$
- Finite Sum ($S_n$): $$S_n = \frac{n}{2}(a_1 + a_n) = \frac{n}{2}(2a_1 + (n-1)d)$$
Geometric Progression (GP)
- $n^{\text{th}}$ Term: $$a_n = a_1 \cdot r^{n-1}$$
- Finite Sum: $$S_n = a_1 \frac{1 - r^n}{1 - r} \quad (r \ne 1)$$
- Infinite Convergent Sum: $$S_\infty = \frac{a_1}{1 - r} \quad (|r| < 1)$$