Question

Write a rule for the nth term of the geometric sequence given a_1=11, a_4=88

Answer 1

The first term of the G.p (a₁)a 11

The =fourth term of the G.p (a₄) = 88

`a_1=11,a_4\text{ = 88}`
`\begin{gathered} a_4=ar^(4-1)=\text{88} \\ ar^3\text{ = 88} \\ a_1\text{ = 11} \end{gathered}`
`\begin{gathered} 11(r)^3\text{ = 88} \\ r^3\text{ = }(88)/(11) \\ r^3\text{ = 8} \\ r^3=2^3 \\ r\text{ = 2} \end{gathered}`

The nth term of the geometric sequence

`\begin{gathered} T_n=ar^(n-1) \\ T_{n\text{ }}=11(2)^(n-1) \end{gathered}`