90,40,15. What is the next number in the pattern and what is the rule for the pattern

a(n+1)=a(n)/2 -5

a1=90

a2=90/2 -5= 45-5= 40

a3=40/2 -5= 20-5= 15

a4=15/2 -5= 7.5-5= 2.5

The next number is 2.5

To find the next number in the pattern and determine the rule, let's analyze the given sequence: 90, 40, 15.

One approach to finding the pattern is to calculate the differences between consecutive terms:

40 - 90 = -50
15 - 40 = -25

By observing the differences, we can see that there is a decreasing pattern. The first difference is -50, and the second difference is -25.

To find the third difference, we subtract:

-25 - (-50) = 25

Now, we can see that the third difference is 25. If we continue this pattern, we can calculate the fourth difference:

25 - (-25) = 50

The pattern for the differences is as follows: -50, -25, 25, 50.

Knowing the pattern of the differences, we can now determine the rule for the original sequence. Since the pattern of differences is increasing by 25 each time, it suggests that the rule for the original sequence involves an increasing quadratic.

Therefore, to find the next term, we need to add the next difference to the previous difference:

50 + 25 = 75

The next number in the pattern is 75.

So, the next number in the sequence is 75, and the rule for the pattern is an increasing quadratic sequence.