Algebra 2

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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 ??

  • Algebra 2 -

    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)=?

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