Question

The explicit rule for a sequence is given.

Answer 1

Answer:

$a_{1} =\frac{2}{5}$ ,Recursive formula is :

$a_{n} =a_{n-1} .5$

Step-by-step explanation:

To find a1 we put n=1 in the given Geometric sequence :

$a_{1} =\frac{2}{5}5^{1-1}$

$a_{1} =\frac{2}{5}$

$a_{2} =\frac{2}{5}5^{2-1} = 2$

Common difference = 2÷$\frac{2}{5}$ = 5.

r=5.

Recursive formula for a geometric sequence is  

$a_{n} =a_{n-1} .r$

Recursive formula is :

$a_{n} =a_{n-1} .5$

Answer 2

Answer: a1=2/5 and an= 5an-1

Just took the test, you're welcome