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

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