Question

20,15,11.25,... find the reclusive and explicit equations

Answer 1

Recursive equation
`T_(1) = 20` and
`T_(n + 1) = T_(n) * (0.75) = 0.75T_(n)` where, n = 1, 2, 3, 4, ........ .

Explicit equation
`T_(n) = 20(0.75)^(n - 1)`.

Explanation:

The given series is an G.P. series and the common ratio is 0.75.

Now, the terms are 20, 15, 11.25, .......

Therefore, the explicit equation of the series will be
`T_(n) = 20(0.75)^(n - 1)`

Again, the recursive equation of the given G.P. series will be

`T_(1) = 20` and
`T_(n + 1) = T_(n) * (0.75) = 0.75T_(n)` where, n = 1, 2, 3, 4, ........