Geometric Sequence

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

The common ratio (r) is the factor by which we multiply each term to get the next term in the sequence.

a₂ = a₁ * r = 5 * 3 = 15.

a₁ represents the first term of the geometric sequence.

The nth term can be found using the formula a_n = a₁ * r^n-1.

The sum S_n of the first n terms is given by S_n = a₁ * (1 - rⁿ) / (1 - r) for r ≠ 1.

The first four terms are 1, 2, 4, 8.

Exponential growth refers to the increase in a quantity where the rate of growth is proportional to the current value, often modeled by geometric sequences.

The common ratio is 2.

a₃ = 10 * (-2)² = 10 * 4 = 40.