Question

Find the 12thterm of the following geometric sequence.5, 10, 20, 40,

Answer 1

Given

5, 10, 20, 40, . . .

SolutionStep1 Find the common ratio(r)
`r=(a_2)/(a_1)=(10)/(5)=2`Step 2

The geometric sequence formula

`a_n=a_1* r^(n-1)`Step 3
`\begin{gathered} r=2,\text{ } \\ a_1=5 \\ n=12 \end{gathered}`Step 4
`\begin{gathered} a_(12)=5*2^(12-1) \\ a_(12)=5*2^(11) \\ a_(12)=10240 \end{gathered}`The final answer The 12th term of the geometric sequence is 10240