The sum of geometric sequence 2,10,50... up to 8 terms is 195312. Therefore, option C is the correct answer.
The given geometric sequence is 2+10+50+250+.....
What is the sum of the geometric sequence formula?
Sum of the geometric sequence is S = a + ar + ar² +....+ [tex]ar^{n-1}[/tex].
The first term of the series is a and the common ratio is r.
The sum of the geometric sequence formula is [tex]S_{n} =\frac{a(r^{n} -1)}{(r-1)}[/tex] .
Now, a=2
To find r,
r = 10/2
r = 5 and n = 8
S = 2 ([tex]5^{8}[/tex]- 1) / (5 - 1)
S = 2(390625 - 1) / 4
S = (390624) / 2
S = 195312
Therefore, the sum of geometric sequence 2,10,50... up to 8 terms is 195312.
To learn more about the geometric sequence visit:
https://brainly.com/question/11266123.
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