Question

Find the sum of the finite geometric sequence whose first term is 0.4, whose ratio is 0.5 and which has five terms.

Answer 1

The formula for the sum of the first n-th term is

`S_n=\frac{a_1(1-r^n)_{}}{1-r}`

where a_1 is the first term, r is the common ratio and n is the nth term. In our case, we have

`\begin{gathered} a_1=0.4 \\ r=0.5 \\ n=5 \end{gathered}`

By substiting these values into the sum formula, we have

`S_5=(0.4(1-0.5^5)=)/(1-0.5)`

which gives

`S_5=(0.4(1-0.03125))/(0.5)`

then, the answer is

`S_5=0.775`