The given series is 128, 64, -32, ...

Finding the pattern:

The first term is 128. To get the next term, we divide the first term by 2. So, the second term is 128/2 = 64.

For the third term, we change the sign of the second term and divide it by 2. So, the third term is -64/2 = -32.

For the fourth term, we divide the third term by 2. So, the fourth term is -32/2 = -16.

Continuing this pattern, we get the following series:

128, 64, -32, -16, 8, -4, 2, -1, 0.5, -0.25, 0.125, -0.0625, ...

Therefore, the 12th term of the series is -0.0625.

Explanation:

The given series follows a specific pattern where each term is derived from the previous term. Understanding the pattern helps to find any term of the series. In this case, the pattern involves dividing the previous term by 2 and changing the sign of the result for every alternate term.

Therefore, to find the 12th term, we need to continue applying this pattern until we reach the 12th term of the series.

Ans:- 16
1) -128/-2 = 64
2) 64/-2 = -32
3) -32/-2= 16