Question

What is the sixth term of the geometric sequence 1024,512,256,…….

Answer 1

Step 1: Write out the nth term of a geometric sequence

`\begin{gathered} a_n=a_1r^(n-1) \\ a_1=\text{first term} \\ r=\text{common ratio} \end{gathered}`

Step 2: Write out the sequence and calculate for a1 and r

`\begin{gathered} 1024,512,256,\ldots \\ a_1=1024 \\ r=(a_2)/(a_1)=(512)/(1024)=(1)/(2) \end{gathered}`

Step 3: Write out the formula for the sixth term and substitute a1 and r

`\begin{gathered} a_6=a_1r^(6-1) \\ =a_1r^5 \end{gathered}`
`\begin{gathered} a_6=1024((1)/(2))^5 \\ =1024((1)/(32)) \\ a_6=32 \end{gathered}`

Hence the sixth term is 32