Find r and a1 for the geometric Sequencewith a3 = 18 and a6= 486show your solution[tex]find \: r \: and \: a1 \: for \: the \: geometric \: sequence \: with \: a3 = 18 \: and \: a6 = 486[/tex]
Answer (1)
SOLUTION:Solving for the common ratio (r) and the first term (a₁) of a geometric sequence• For r[tex]\begin{aligned} a_n & = a_mr^{n - m} \\ a_6 & = a_3r^{6 - 3} \\ 486 & = 18r^3 \\ 18r^3 & = 486 \\ \frac{18r^3}{18} & = \frac{486}{18} \\ r^3 & = 27 \\ \sqrt[3]{r^3} & = \sqrt[3]{27} \\ r & = \boxed{3} \end{aligned}[/tex]• For a₁In this case, we chose 3 as the value of n because we will use the third term as the nth term here.[tex]\begin{aligned} a_n & = a_1r^{n - 1} \\ a_3 & = a_1r^{3 - 1} \\ 18 & = a_1(3^2) \\ 18 & = 9a_1 \\ 9a_1 & = 18 \\ \frac{9a_1}{9} & = \frac{18}{9} \\ a_1 & = \boxed{2} \end{aligned}[/tex]Hence, the values of r and a₁ are 3 and 2, respectively.
