Question

Hiroki and Mapiya were asked to find an explicit formula for the sequence 125,25,5,1,.

Answer 1

Answer:

Formula for the sequence

${5}^{4 - n}$

n = nth term of the series(1,2,3,4....)

Step-by-step explanation:

125, 25, 5, 1,....

Here a = 125

a2 = 25

a3 = 5

a4 = 1

$\frac{a2}{a} = \frac{25}{125} = \frac{1}{5} \\ \frac{a3}{a2} = \frac{5}{25} = \frac{1}{5} \\ \frac{a4}{a3} = \frac{1}{5}$

Since, this series has a common multiplier

Therefore, it is a Geometric Progression(G.P) Series

The General Equation for G.P is

$a. {r}^{n - 1}$

Here, a= First term of the series = 125

r = common multiplier = (1/5)

n = nth term of the series(1,2,3,4

So, the explicit formula for the series is

$125. ({ \frac{1}{5} })^{n - 1} = {5}^{3} . {5}^{1 - n} = {5}^{4 - n}$