Find an explicit formula for An

Question

Given the geometric sequence: 14, (140/11), (1400,121)....

Find an explicit formula for A_n

A_n=

Find A₁₁

Answer 1

“Given the geometric sequence:
14, (140/11), (1400/121),…
Find an explicit formula for An
Find A11”

r = (140/11)/14 = (1400/121)/(140/11) = 10/11

An = 14(10/11)^(n-1), n a positive integer

[Note: 0 is neither positive nor negative.]

A11 = 14(10/11)^(11-1)

A11 = 14(10/11)^10 = 14*10^10/11^10

A11 = (140,000,000,000)/(25,937,424,601)

A11 ≈ 5.39760605201344

Answer 2

 14, 140/11, 140/121

 

  a_n = 14 ( 10/11) ^(n - 1)