When is a sequence geometric? when each term is multiplied by the same number to get the next term when there is a common difference between terms when the sequence increases or decreases in a linear pattern when the ratios between consecutive terms are reciprocals

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Braeden Velasquez

Mathematics

10 January, 16:48

When is a sequence geometric? when each term is multiplied by the same number to get the next term when there is a common difference between terms when the sequence increases or decreases in a linear pattern when the ratios between consecutive terms are reciprocals

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Sofia Merritt · Answer 1

A geometric sequence when each term is a constant multiple (or fraction) with respect to the previous term, called the common ratio. So the first statement is true. Mathematically:

a (2) / a (1) = a (3) / a (2) = a (4) / a (3) ... = r, the constant called the common ratio.

Any geometric sequence can be expressed as:

a (n) = ar^ (n-1), a=initial term, r=common ratio, n=term number.