CCSS.HSF.IF.A.3.Q.A1.SF.6 - Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

The given sequence is a geometric sequence in the form 1, -1, 1, -1, 1, -1, . . . because the common ratio is -1.

A geometric sequence is of the form a, ar, ar^{2}, .... ar^{n}

The expression to denote the sequence would be a_{n} = ar^{n-1}where r is the common ratio, a is the first term, ar^{n} is the n^{th} term or the last term and ar^{n-1} is the n-1^{th} (the term before the last term)

So, when n = 1 plugging in n = 1 in the above expression we get, a_{1} = a.r^{1-1} = ar^{0} = 1 which we already know.

To find the 8^{th} term in the series, plug n = 8, in the above expression to get

a_{8} = ar^{7} = 1 \times (-1)^{7} = -1

So, the 8^{th} term is -1.