Write the series whose nth term is 5*2^( n+1). The series is a geometric progression ?

We'll associate the formula for the n-th term of the
sequence with the given expresion:

an =
5*2^(n+1)

Now, we'll create the sequence, by giving values
to n.

For n = 1=>a1= 5*2^(1+1) = 5*2^2 = 5*4 =
20

For n = 2=>a2 = 5*2(2+1) = 5*2^3 = 5*8 =
40

For n = 3=>a3 = 5*2^(3+1) = 5*2^4 = 5*16 =
80 

..................................................................................

The
terms of the sequence are:

20, 40, 80,
....................

Now, we'll create ratios from 2
consecutive terms:

a2/a1 = 40/20 =
2

a3/a2 = 80/40 =
2

................................

We
notice that the series is a geometric series, with the common ratio r =
2.