What is the pattern rule for 1122, 1112, 1101, 1091?
well, the first three digits are 112,111,110,109, ...
Not sure why the last digit repeats in pairs, but I guess the next two terms could be 1080, 1070
No obvious pattern, but
the difference between first and second is -10
the difference between the 2nd and third is -21
the difference between the 3rd and the 2nd is -11
the difference between the 4th and the 3rd is -10
we could "force" a pattern on the numbers by assuming they are the
results of a cubic function
f(x) = ax^3 + bx^2 + cx + d , and let x = 0,1,2,3
f(0) = 0+0+0+d = 1122 , so d = 1122
f(1) = a + b + c + 1122 = 1112
or a+b+c = -10
f(2) = 8a + 4b + 2c + 1122 = 1101
8a + 4b + 2c = -21
f(3) = 27a + 9b + 3c + 1122 = 1091
27a + 9b + 3c = -31
so term(n) = (1/3)n^3 - (3/2)n^2 - (53/6)n + 1122
for n = 0, 1, 2, 3 to get your 4 terms
check: term(3) should give us 1091
term(3) = (1/3)(27) - (3/2)(9) - (53/6)(3) + 1122
= 9 - 27/2 - 53/2 + 1122
= 1091
term(2) = (1/3)(8) - (3/2)(4) - (53/6)(2) + 1122
= 1101
Looking good
I still believe you have a typo somewhere, so I was just having some fun with this.
To determine the pattern rule for the given sequence, we need to examine the numbers and look for any discernible pattern or trend.
In this sequence: 1122, 1112, 1101, 1091, we can observe the following:
- In the first number (1122), the first two digits (11) are repeating.
- In the second number (1112), the first two digits (11) are still repeating, but the last two digits are decreasing by 1 (from 22 to 12).
- In the third number (1101), the first two digits (11) are repeating again, and both the last two digits are decreasing by 1 (from 12 to 01).
- In the fourth number (1091), the first two digits (11) are repeating once more, and only the last digit is decreasing by 1 (from 01 to 91).
Based on these observations, we can conclude that the pattern rule for this sequence is:
- The first two digits (11) remain constant throughout the sequence.
- The last two digits follow a decreasing pattern, where the first number has a difference of 10 from the previous number, and the second number has a difference of 1 from the previous number.
Therefore, the pattern rule for the given sequence is:
- Start with the constant number (11) and subtract 10 from the last two digits for each subsequent number.
To verify this rule, you can continue the pattern to find the next number in the sequence:
1080 (11 - 10 = 01, 01 - 1 = 00).
Please note that pattern rules are not always unique, and different patterns may be possible. However, based on the given sequence, the rule of subtracting 10 and 1 appears to be the most prevalent.