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

Solution

Step 1

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

$\begin{gathered} T_n\text{ = \lparen1.06\rparen}^{n-1} \\ Common\text{ ratio = }\frac{2^{nd}term}{1^{st}term} \end{gathered}$

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

$Common\text{ ratio r = }\frac{1.06}{1}\text{ = 1.06}$

Final answer