what are the rules for these two problem? I can not figure it out. I spent 30 minutes trying to figure it out
1, 10
2, 9
3, 8
4, 7
lI know the left is increasing by one and the right is decreasing by one but I can't find an equation for this.
and the second one is
0, -5
1, -12
2, -17
3, -22
4, -27
I know the
Xn = 11 - n
Xo = -5 (I think the first one should be -7)
Xn = -7 - 5 n
or for the second one
Xn+1 = Xn -5
again the first one does not fit
For the first problem:
To find the rule for the given sequence (1, 10), (2, 9), (3, 8), (4, 7), you have correctly observed that the left column is increasing by one while the right column is decreasing by one. Based on this pattern, it appears that the formula is:
Left column: n (where n represents the position of the pair in the sequence)
Right column: 11 - n
So, for example, for the first pair (1, 10), 1 is the first position in the sequence, and if you substitute n=1 into the formula, you get 11-1=10. Similarly, for the second pair (2, 9), substituting n=2 into the formula gives you 11-2=9, and so on.
For the second problem:
To find the rule for the given sequence (0, -5), (1, -12), (2, -17), (3, -22), you can observe that the left column is increasing by one, but the right column does not follow a simple arithmetic pattern. In this case, you need to find a different approach.
By analyzing the sequence more closely, you can deduct that the right column values are decreasing by 5 units each time the left column increases by 1. Therefore, the formula for the right column can be written as:
Right column: -5n – 5
For instance, for the third pair (2, -17), the left column value is 2, and substituting n=2 into the formula gives you -5(2) – 5 = -10 – 5 = -15, which matches the given value of -17.
By using this formula for the right column, you can find the corresponding values for any given pair in the sequence.