Question

What is the first term of the geometric sequence whose fifth term is 1/24 and tenth term is 1/768

Answer 1

An=a1r^(n-1)

given
a5=1/24
a10=1/768

we know that
a5=1/24=a1r^(5-1) and
a10=1/768=a1r^(10-1)

so
1/24=a1r^4
1/768=a1r^9

(a1r^9)/(a1r^4)=r^5=(1/768)/(1/24)=1/32

r^5=1/32
take 5th root of both sides
r=1/2

we have
a5=a1r^4=1/24
evaluate r^4 or (1/2)^4
1/16
a1(1/16)=1/24
times both sides by 16/1
a1=16/24
a1=2/3

the first term is 2/3