# Find the common ratio and the first term in the geometric progressions where A) The 2nd term is 4 and the 5th term is 108

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Expert Answers

jeew-m | Certified Educator

nth term `T_n` of a geometric series with first term a and common ratio r is given by;

`T_n = ar^(n-1)`

`T_2 = ar^(2-1)`

`4 = ar ----(1)`

`T_5 = ar^(5-1)`

`108 = ar^4----(2)`

(2)/(1)

`108/4 = r^4/r`

`27 = r^3`

`3^3 = r^3`

`3 = r`

From (1)

`4 = ar`

`4 = a*3`

`4/3 = a`

*So the first term is 4/3 and the common ratio is 3.*