Question

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

Answer 1

Answer:

Recursive equation $T_{1} = 20$ and $T_{n + 1} = T_{n} \times (0.75) = 0.75T_{n}$ where, n = 1, 2, 3, 4, ........ .

Explicit equation $T_{n} = 20(0.75)^{n - 1}$.

Step-by-step 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 $T_{n + 1} = T_{n} \times (0.75) = 0.75T_{n}$ where, n = 1, 2, 3, 4, ........