The common ration of the sequence is

\(\displaystyle{r}={\frac{{−{20}}}{{{4}}}}=−{5}{r}\)

\(\displaystyle={\frac{{{100}}}{{−{20}}}}=−{5}\)

Since, the value of the \(\displaystyle{r}{ < }{1}\), the formula for the sum of the n term of the series is:

\(\displaystyle{S}_{{n}}={\frac{{{a}{\left({1}−{r}{n}\right)}}}{{{1}−{r}}}}\)

Then, sum of first five terms is

\(\displaystyle{S}_{{5}}={\frac{{{4}{\left({1}−{\left(−{5}\right)}{\left\lbrace{5}\right\rbrace}\right)}}}{{{1}−{\left(−{5}\right)}}}}\)

\(\displaystyle={\frac{{{4}{\left({1}+{3125}\right)}}}{{{1}+{5}}}}\)

\(\displaystyle={4}{\frac{{{3126}}}{{{6}}}}\)

\(\displaystyle={4}{\left({521}\right)}={2084}\)

Thus, the sum of the first five terms is 2084.

\(\displaystyle{r}={\frac{{−{20}}}{{{4}}}}=−{5}{r}\)

\(\displaystyle={\frac{{{100}}}{{−{20}}}}=−{5}\)

Since, the value of the \(\displaystyle{r}{ < }{1}\), the formula for the sum of the n term of the series is:

\(\displaystyle{S}_{{n}}={\frac{{{a}{\left({1}−{r}{n}\right)}}}{{{1}−{r}}}}\)

Then, sum of first five terms is

\(\displaystyle{S}_{{5}}={\frac{{{4}{\left({1}−{\left(−{5}\right)}{\left\lbrace{5}\right\rbrace}\right)}}}{{{1}−{\left(−{5}\right)}}}}\)

\(\displaystyle={\frac{{{4}{\left({1}+{3125}\right)}}}{{{1}+{5}}}}\)

\(\displaystyle={4}{\frac{{{3126}}}{{{6}}}}\)

\(\displaystyle={4}{\left({521}\right)}={2084}\)

Thus, the sum of the first five terms is 2084.