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