Frequently Asked Questions
What is the difference between an arithmetic and geometric sequence?
Arithmetic sequences add a constant difference d each term (2, 5, 8, 11). Geometric sequences multiply by a constant ratio r (3, 6, 12, 24).
What is the formula for the nth term?
Arithmetic: aₙ = a₁ + (n − 1)d. Geometric: aₙ = a₁ · r^(n−1). Plug in n to jump directly to any term without listing them all.
How do I sum the first n terms?
Arithmetic: Sₙ = n(a₁ + aₙ)/2. Geometric: Sₙ = a₁(1 − rⁿ)/(1 − r) for r ≠ 1. The infinite geometric sum converges only if |r| < 1.
Where do sequences appear in real life?
Compound interest is geometric, loan amortization uses sequences, population growth models them, and the Fibonacci sequence appears in biology and finance.
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