In a geometric sequence, the ratio between two consecutive numbers is same.

ratio r = `(a2)/(a1)`

To find nth term of the sequence we use an formula. `an = a1 . r^(n-1)`

1. 2500, 500, 100,.....

here r =

We need to find `a4, a5` and `a6` of the sequence

`a4 = a1. r^(4-1) = 2500 . (1/5)^3 = 2500/125 = 20`

`a5 = a1. r^(5-1) = 2500 .(1/5)^4 = 2500/625 = 4`

`a6 = a1. r^(6-1) = 2500 .(1/5)^5 = 2500/3125 = 4/5 = 0.8`

`therefore` the next three terms of the sequence are **20, 4, 4/5**

2. 2, 6,...

(The entire section contains 2 answers and 190 words.)

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