given two terms from a geometric sequence, identify the first term and the common ratio: a7 = 81 and a10 = 3.

An=a1(r)^(n-1)

a7=a1(r)^(7-1)=a1r^6
a10=a1(r)^(10-1)=a1r^9
a10/a7=(a1r^9)/(a1r^6)=r^3
a10/a7=3/81=r^3

3/81=1/27
1/27=r^3
cube root both sides
1/3=r

subsitute

a7=a1r^6
81=a1(1/3)^6
81=a1(1/729)
times 729 both sides
59049=a1

first term is 59049
common ratio is 1/3