The sum of first 8 terms of series is -130208
Solution:
Given that,
2 - 10 + 50 - 250 , ....
n = 8
Find the common ratio between a term and its previous term
[tex]r = \frac{-10}{2} = -5\\\\r = \frac{-250}{50} = -5[/tex]
Thus common ratio is same
This is a geometric series
The sum of terms of geometric sequence is given as:
[tex]S_n = \frac{a_1(1-r^n)}{1-r}[/tex]
Where,
r is the common ratio
n is the nth term
[tex]a_1[/tex] is the first term of series
From series,
[tex]a_1 = 2\\\\r = -5\\\\n = 8[/tex]
Therefore,
[tex]S_8 = \frac{2 \times (1 - (-5)^8)}{1-(-5)}\\\\S_8 = \frac{2 \times (1-390625)}{6}\\\\S_8 = -130208[/tex]
Thus sum of first 8 terms of series is -130208
