Answer:
So, the eighth term of the series is 640.
Explanation:
The given series appears to be a geometric progression (GP) where each term is obtained by multiplying the previous term by a common ratio. To find the common ratio (r), we can divide any term by its previous term:
- r = 10 / (-5) = -2
- r = (-20) / 10 = -2
- r = 40 / (-20) = -2
Since the common ratio between consecutive terms is -2, this series is indeed a geometric progression.
To find the eighth term of the series, we can use the formula for the nth term of a geometric progression:
Tn = a * r^(n-1)
Where:
- Tn is the nth term.
- a is the first term (-5 in this case).
- r is the common ratio (-2 in this case).
- n is the term number we want (8th term in this case).
Now, plug in the values:
T8 = (-5) * (-2)^(8-1)
T8 = (-5) * (-2)^7
Calculate the value:
T8 = (-5) * (-128)
T8 = 640
So, the eighth term of the series is 640.