Given a geometric sequence a4 =125 and a10 = 125/64

Question

Show the appropriate work to find each of the following:

a)r =

b)a1 =

c)an =

d)a14 =

Answer 1

a)

a₁r⁴=125

a₁= 125/r⁴

a₁r¹⁰= 125/64

(125/r⁴) r¹⁰= 125/64

r⁶= 1/64

r = 1/2

b) a₁= 125/r⁴= 125(2)⁴ = 2000

c) a_n = a₁rⁿ = 2000(1/2)ⁿ

d) a₁₄ = 2000(1/2)¹⁴ = 2000/16384 = 125/1024