Pick AP or GP, enter the first term and the common difference or ratio, and get the nth term and the sum of n terms instantly.
AP & GP Calculator
How It’s Calculated
Arithmetic Progression: each term adds a fixed common difference d. The nth term is a + (n−1)d, and the sum of n terms is n/2 × (2a + (n−1)d).
Geometric Progression: each term multiplies by a fixed common ratio r. The nth term is a×r(n−1), and the sum of n terms is a×(rn−1)/(r−1) when r ≠ 1 — or simply a×n when r = 1.
Worked Example
AP with a=2, d=3, n=5: a₅ = 2+(5−1)×3 = 14. S₅ = 5/2×(2×2+4×3) = 5/2×16 = 40.
GP with a=2, r=3, n=5: a₅ = 2×3⁴ = 162. S₅ = 2×(3⁵−1)/(3−1) = 2×242/2 = 242.
Frequently Asked Questions
Q: How do I know if a sequence is AP or GP?
Check consecutive terms: if the difference between them is constant, it’s AP. If the ratio between them is constant, it’s GP.
Q: What if r = 1 in a GP?
Every term is identical to a, so the sum is simply a×n — the standard GP sum formula would divide by zero otherwise.
Sequences & Series is a reliable mark-scorer in 1st PUC when the formulas are genuinely understood, not just memorised. See how Daniel Classes teaches 1st and 2nd PUC Mathematics →