Answer
We have a geometric sequence and the sum is:
$S_n=\dfrac{25(1−(0.4)^n)}{(1−0.4)}$
Work Step by Step
For the sequence to be geometric, the quotient of all consecutive terms must be constant.
Here, we have: $\dfrac{a_{2}}{a_1}=\dfrac{10}{25}=0.4$ and $\dfrac{a_{3}}{a_2}=\dfrac{4}{10}=0.4$
This shows that the quotient of all consecutive terms is constant and thus it is a geometric sequence.
The sum of $n$ terms of a geometric sequence is given by the formula:
$S_n=\dfrac{a_1(1−r^n)}{(1−r)}$
where $a_1$ is the first term and $r$ is the common ratio.
Therefore, the sum is: $S_n=\dfrac{25(1−(0.4)^n)}{(1−0.4)}$
