Question

What is the explicit formula for the sequence that is associated with the table?

Answer 1

Answer:

see explanation

Step-by-step explanation:

Consider the values of y

$\frac{2}{5}$, 2, 10, 50

Consider the ratio between consecutive terms

2 ÷ $\frac{2}{5}$ = 5

10 ÷ 2 = 5

50 ÷ 10 = 5

Since the ratio is common then the terms form a geometric sequence

The n th term of a geometric sequence is

$a_{n}$ = a$(r)^{n-1}$

where a is the first term and r is the common ratio, hence

$a_{n}$ = $\frac{2}{5}$$(5)^{n-1}$ ← explicit formula