Question

I A Series is given by-5+10-20 + 40+

a Identify the Series
find the eight term of the Series

Answer 1

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.