Answer
The first four terms of the series $\sum\limits_{i=1}^{6}{{{2}^{i}}}$ are $2;{{2}^{2}};{{2}^{3}};{{2}^{4}}$. The common ratio is 2.
Work Step by Step
In order to find the terms of the series $\sum\limits_{i=1}^{6}{{{2}^{i}}}$, we have to replace i in the expression ${{2}^{i}}$ with all the consecutive integers from 1 to 6.
Hence, the first term is obtained as $ i~=\text{ }1,~{{2}^{1}}$
Then, the second term is obtained as i = 1, ${{2}^{2}}$
Similarly the third term is obtained as i = 1, ${{2}^{3}}$
And the fourth term is obtained as i = 1, ${{2}^{4}}$
