What is the explicit rule for the nth term of the sequence 5, 25, 125, 625?

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The given sequence is: 5, 25, 125, 625. To find the explicit rule for the nth term, let’s first observe the pattern in the sequence.

We can see that each term is a power of 5:

  • The first term (n=1) is 5^1 = 5
  • The second term (n=2) is 5^2 = 25
  • The third term (n=3) is 5^3 = 125
  • The fourth term (n=4) is 5^4 = 625

From this observation, we can conclude that the nth term of the sequence can be expressed explicitly as:

an = 5n

where n is the position of the term in the sequence. So, for any term in this geometric sequence, simply replace n with the term’s position to find its value.

For example:

  • For n=1: a1 = 51 = 5
  • For n=2: a2 = 52 = 25
  • For n=3: a3 = 53 = 125
  • For n=4: a4 = 54 = 625

This rule holds for all positive integer values of n.

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