Question

A recursive rule for a geometric sequence is a1=8; an=3/4a n−1 . What is the explicit rule for this sequence?

Answer 1

A(n) =(3/4)x a(n-1)


for n =1==> a₁ =8
Give for n, the value 2,3,4 etc.

for n=2==>a₂ = 3/4(a₁) = 3/4 (8) = 6
for n=3 ==>a₃ =3/4(a₂) = 3/4(6) = 9/2
for n=4 ==>a₄ =3/4(a₃) = 3/4(9/2)
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and for n=n ==>a(n) =(3/4)(a(n-1)