Question

A geometric sequence is defined by the recursive formula t1 = 64, tn = tn - 1 2 , where n ∈N and n > 1. The sequence is

Answer 1

a(n)=64(2^(n-1))

...................... oh you want to change is so n>1....okay...

64=a(2^n) since the first term is 64...

64=2a so a=32 then...

a(n)=32(2^n)

Answer 2

Answer with explanation:

⇒Formula defining Geometric Sequence and the sequence is

Let a be the first term and r be the common difference.

`t_(1)=64\\\\t_(n)=(t_(n-1))^2\\\\ar^(n-1)=(ar^(n-2))^2\\\\a_(n)=ar^(n-1)\\\\ar^(n-1)=a^2r^(2n-2)\\\\a^(2-1)r^(2n-2-n+1)=1\\\\a*r^(n-1)=1\\\\64*r^(n-1)=1\\\\r^(n-1)=(1)/(64)\\\\r^(n-1)=[(1)/(4)]^3\\\\r=(1)/(4)\\\\ \text{So,the sequence is}\\\\64,64*(1)/(4),64*[(1)/(4)]^2,64*[(1)/(4)]^3,64*[(1)/(4)]^4,.......\\\\=64, 16,4,1,(1)/(4),(1)/(16),.....`