Recursive Formula

Question

Using the recursive formula of a geometric sequence, find the first five terms: An=An-1 • 2
Please explain how. Thank u!

Answer 1

a_n = 2a_n-1

 

To find subsequent terms, we first need at least one term.

 

Example: Given a₁ = 5 and a_n = 2a_n-1

a₁ = 5

a₂ = 2(a₁) = 2(5) = 10

a₃ = 2(a₂) = 2(10) = 20

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It is also possible to work backwards.  Given a_n = 2a_n-1 then a_n-1= a_n/2

 

If we have a₄ = 40

a₃ = 40/2 = 20

a₂ = 20/2 = 10

a₁ = 10/2 = 5