Question

Find the specified term of each geometric sequence

ab^2, a^2b^5, a^3B^8, ...; t25
really stumped.

I know that r= (a^2b^5)/ab^2 but I don't know what to do next.

ab^2 ((a^2b^5)/ab^2)^n-1 ??

Answer 1

r= (a^2b^5)/ab^2 = ab³

therefore
t(n)=a^n b^(3n-1)
Check:
t(1)=a^1b^(3-1)=ab²
t(2)=a^2b^(2*3-1)=a²b^5
t(3)=a^3b^(3*3-1)=a³b^8
...
So
t(25)=?