Answer:
Sum of first n terms = a1 * (r^n - 1) / (r - 1).
Step-by-step explanation:
Sum of n terms = Sn = a1 * (r^n - 1) / (r - 1) where a1 = first term , r = common ratio
and n is the number of terms.
The sum of the first n terms of a geometric sequence can be given by the formula [tex]\sum_{k=0}^{n-1}(ar^k) = a\dfrac{(1-r^n)}{(1-r)}, where (r\leq 1)[/tex].
A geometric sequence is a sequence in which the next term of the sequence is a result of the product of the previous term and the common ratio.
for example,
S = 1, 2, 4, 8, 16, ..........
the above series is a geometric series with the common ratio of 2,
every next term is the product of the previous term and 2.
The Sum of a geometric sequence is given by the formula,
[tex]\sum_{k=0}^{n-1}(ar^k) = a\dfrac{(1-r^n)}{(1-r)}, where (r\leq 1)[/tex]
[tex]\sum_{k=0}^{n-1}(ar^k) = a\dfrac{(r^n-1)}{(r-1)}, where (r> 1)[/tex]
where,
a is the first term of the series,
r is the common ratio,
n is the [tex]\bold{n^{th}}[/tex] term.
If n is equal to infinity,
[tex]\sum_{k=0}^{n=\infty}(ar^k)=a(\dfrac{1}{1-r})[/tex]
Hence, the sum of the first n terms of a geometric sequence can be given by the formula [tex]\sum_{k=0}^{n-1}(ar^k) = a\dfrac{(1-r^n)}{(1-r)}, where (r\leq 1)[/tex].
Learn more about Geometric progression:
https://brainly.com/question/14320920
