Geometric Sequences Flashcards

A sequence where each term is found by multiplying the previous term by a constant value called the common ratio.

The constant value by which each term in a geometric sequence is multiplied to get the next term.

Divide any term in the sequence by the previous term.

The nth term of a geometric sequence is given by the formula a × r^(n-1), where a is the first term and r is the common ratio.

The first term in a geometric sequence, represented by 'a' in the nth term formula.

a × r^(n-1), where a is the first term, r is the common ratio, and n is the term number.

2, 6, 18, 54... (common ratio is 3).

Check if the ratio between consecutive terms is constant.

The sum of the first n terms is given by the formula S_n = a(1 - r^n) / (1 - r), where r ≠ 1.

If |r| < 1, the sum to infinity is S = a / (1 - r).