# Arithmetic and geometric sequences: Identifying and writing an explicit rule

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### Question Description

The sequences below are either arithmetic or geometric.  For each sequence, determine whether i it is arithmetic or geometric, and write the formula for the nth term an of that sequence

TYPE               nth term formula

-6, -8, -10, ...

27, -9, 3, ...

abotsi55
School: Purdue University

-6,-8,-10 is an arithmetic sequence. The first term is a1=-6. The common difference is d=-2.

The n-th term is a(n) = a1 + (n-1)d. Therefore

a(n) = -6 + (n-1)(-2) = -4 - 2n.

n=1:  a(1) = -4 -2(1) = -6

n=2: a(2) = -4 - 2(2) = -8

-----------------

27,-9,3, ... is a geometric sequence.

The first term is a=27. The common ratio is r = -1/3.

The n-th term is a(n) = 27(-1/3)^(n-1) = -81(-1/3)^n

n=1: a(1) = -81(-1/3) = 27

n=2: a(2) = -81(-1/3)^2 = -9

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