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

Expert Answers
hala718 eNotes educator| Certified Educator

an = 5*2^(n+1)

a1 = 5*2^2 = 4*4 = 20

a2 = 5*2^3 = 5*8 = 40

a3= 5*2^4 = 5*16 = 80

a4= 5*2^5 = 5*32 = 160

Then:

20, 40, 80, 160, ..... is a Geometric Progression with ratio between terms is r = 2

 

giorgiana1976 | Student

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 

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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

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