high School⏱ 3 min

Geometric Sequence

Each term = previous × q

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1.0a12.0a24.0a38.0a416.0a532.0a664.0a7×2
a₁ = 1
Common ratio q = 2
n = 7
an=a1⋅qn−1=1⋅2n−1a_n = a_1 \cdot q^{n-1} = 1 \cdot 2^{n-1}

a7 = 64.000

Geometric sequence: each term is q times the previous. If |q|>1 it grows, if |q|<1 it decays to zero. Foundation of exponential growth and compound interest.