An explicit pattern rule uses the term number of a pattern in order to not only continue the pattern, but to find the value for any given term in the pattern.
If we had the number pattern: 5, 7, 9. . .
T1 = 5, T2 = 7, T3 = 9 THINK: What is the relationship between the term number and its value?
T# x 2 + 3 See if your rule works.
For T4 it would be 4 x 2 + 3 = 11 so term 4 would have a value of 11
for T5 it would be 5 x 2 + 3 = 13 so term 5 would have a value of 13
The explicit rule seems to work because the common difference between the values is always 2:
5, 7, 9, 11, 13...
If you wanted to find any random term in this pattern you just have to use your explicit rule.
Try term number 20
The rule is T# x 2 + 3 so "plug in" the number 20. 20 x 2 + 3 = 40 +3 = 43
Term 20 would be 43.
If we had the number pattern: 5, 7, 9. . .
T1 = 5, T2 = 7, T3 = 9 THINK: What is the relationship between the term number and its value?
T# x 2 + 3 See if your rule works.
For T4 it would be 4 x 2 + 3 = 11 so term 4 would have a value of 11
for T5 it would be 5 x 2 + 3 = 13 so term 5 would have a value of 13
The explicit rule seems to work because the common difference between the values is always 2:
5, 7, 9, 11, 13...
If you wanted to find any random term in this pattern you just have to use your explicit rule.
Try term number 20
The rule is T# x 2 + 3 so "plug in" the number 20. 20 x 2 + 3 = 40 +3 = 43
Term 20 would be 43.