If the sum of the coefficients in the expansion of $(1+2x{)}^n$ is $2,187$, the greatest  term in the expansion, if $x=\frac{1}{2}$ is/are

Substituting $x=1$ for the sum of coefficients of the given expansion.
$3^n=2187$
${\log }_3(n)={\log }_3(2187)$
$n=7$
Hence the expansion will be of the form $(1+2x{)}^7$
Now there will be total of 8 terms, and for $x=\frac{1}{2}$ the value of a term will only depend on its binomial coefficient.
Therefore the greatest terms will be the set of two middle terms. which are the 4th term and the 5th term.