What is the 5th term in the geometric sequence 0125, 025, 05?

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To find the 5th term in the geometric sequence 0125, 025, 05, we first need to identify the pattern in the sequence. The given terms can be expressed as numbers: 125, 25, and 5.

A geometric sequence is defined by the property that each term is obtained by multiplying the previous term by a constant, known as the common ratio (r). Let’s find the common ratio (r) for this sequence:

  • First term (a1): 125
  • Second term (a2): 25
  • Third term (a3): 5

The common ratio (r) can be calculated as follows:

  • r = a2 / a1 = 25 / 125 = 0.2
  • r = a3 / a2 = 5 / 25 = 0.2

Since the common ratio is consistent, we can confirm that it is

  • r = 0.2

Now that we have the common ratio, we can find the terms of the sequence using the formula for the nth term of a geometric sequence, which is:

an = a1 * r(n-1)

We need to calculate the 5th term (n = 5):

a5 = 125 * (0.2)(5-1)
              = 125 * (0.2)4
              = 125 * (0.0016)  
              = 0.2

Therefore, the 5th term in the geometric sequence is 0.2.

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