Question

Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 2,1,0.5,0.25, . . . . . .

Answer 1

It is a geometric sequence. The next two terms are: 0.125, 0.0625

The given sequence is:

2, 1, 0.5, 0.25, . . . .

Let a(n) be the nth term, then in the above sequence

a(1) = 2

a(2) = 1

a(3) = 0.5

a(4) = 0.25

Notice that:

a(2) = a(1) x 0.5

a(3) = a(2) x 0.5

a(4) = a(3) x 0.5

A sequence, of which its next term is obtained by multiplying the previous term by a constant is called a geometric sequence. The constant is called the ratio.

Therefore this is a geometric sequence with r = 0.5

To find the next two terms, continue the multiplication process:

a(5) = a(4) x 0.5 = 0.25 x 0.5 = 0.125

a(6) = a(5) x 0.5 = 0.125 x 0.5 = 0.0625

Learn more about sequences here:

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