Question

Find the common ratio and write out the first four terms of the geometric sequence (1.06)n−1 Common ratio is a1= a2= a3= a4=

Answer 1

Step 1

Write the nth term ex[pression and the common ratio formula.

`\begin{gathered} T_n\text{ = \lparen1.06\rparen}^(n-1) \\ Common\text{ ratio = }(2^(nd)term)/(1^(st)term) \end{gathered}`

Step 2

`\begin{gathered} T_1\text{ = \lparen1.06\rparen}^(1-1)\text{ = 1} \\ T_2\text{ = \lparen1.06\rparen}^(2-1)\text{ = 1.06} \\ T_3\text{ = \lparen1.06\rparen}^(3-1)\text{ = \lparen1.06\rparen}^2\text{ = 1.1236} \\ T_4\text{ = \lparen1.06\rparen}^(4-1)=\text{ \lparen1.06\rparen}^3\text{ = 1.191016} \end{gathered}`

Step 3

`Common\text{ ratio r = }(1.06)/(1)\text{ = 1.06}`

Final answer