If you are good at writing explicit definition (rule) for the nth term of a geometric sequence Please Help!! Show work

  an = (5/16)2^(n -1)

Step-by-step explanation:

The explicit formula for the n-th term of a geometric sequence is ...

  an = a1·r^(n-1)

Filling in the given values, we get two equations in a1 and r:

  a5 = 5 = a1·r^(5 -1)

  a9 = 80 = a1·r(9 -1)

Dividing the second equation by the first gives ...

  80/5 = (a1·r^8)/(a1·r^4)

  16 = r^4

  2 = r . . . . . . . . because we know 2^4 = 16. You could also solve using logarithms

Then we can find a1 from ...

  5 = a1·r^4 = 16·a1

  5/16 = a1

The explicit formula is ...

  an = (5/16)2^(n -1)

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The above formula matches the form of the equation usually expected. However, we can make the fraction go away by adjusting the exponent:

  an = 5(2^-4)(2^(n-1))

  an = 5·2^(n -5)