Answer
Find out the the value of the fourth term in a geometric sequence for which
[tex]a_{1} = 10\ and\ r =0.5[/tex]
To proof
The formula for the general term for each geometric sequence is
[tex]a_{n} = a_{1} r^{n-1}[/tex]
where
[tex]a_{1} = first\ term,\ r = common\ ratio[/tex]
Put n= 4
[tex]a_{4} = 10\times(0.5)^{4-1}[/tex]
[tex]a_{4} = 10\times(0.5)^{3}[/tex]
[tex]a_{4} = 10\times0.125[/tex]
Solving
[tex]a_{4} = 1.25[/tex]
The value of the fourth term in a geometric sequence is 1.25 .
Hence proved
