Writing A Formula From A
Sequence
Writing A Formula From A Sequence:
Examples;
Determine the 100th term of the following.
1.) 7 , 10, 13, 16, ..., _____
Solution:
Using the difference table does not apply to this problem since the 100th term
should be found.
We need to write a formula that will help us solve this problem.
Step 1: Find the difference in the pattern:
10 - 7 = 3
13 - 10 = 3
16 - 13 = 3
Since 3 is the first difference we can have an equation: 3n
Step 2: Use the equation formulated in step 1.
In 3n let n be any real number from 1 to infinity.
if n =1 then 3n = 3
if n = 2 then 3n = 6
if n = 3 then 3n = 9
if n = 4 then 3n = 12
Step 3: Use the given sequence then subtract the sequence formulated from 3n.
7 10 13 16
- 3 6 9 12
4 4 4 4 the difference is +4
Step 4: Then the formula is 3n + 4.
Step 5: Use the formula to solve for the missing term.
Sequence
Writing A Formula From A Sequence:
Examples;
Determine the 100th term of the following.
1.) 7 , 10, 13, 16, ..., _____
Solution:
Using the difference table does not apply to this problem since the 100th term
should be found.
We need to write a formula that will help us solve this problem.
Step 1: Find the difference in the pattern:
10 - 7 = 3
13 - 10 = 3
16 - 13 = 3
Since 3 is the first difference we can have an equation: 3n
Step 2: Use the equation formulated in step 1.
In 3n let n be any real number from 1 to infinity.
if n =1 then 3n = 3
if n = 2 then 3n = 6
if n = 3 then 3n = 9
if n = 4 then 3n = 12
Step 3: Use the given sequence then subtract the sequence formulated from 3n.
7 10 13 16
- 3 6 9 12
4 4 4 4 the difference is +4
Step 4: Then the formula is 3n + 4.
Step 5: Use the formula to solve for the missing term.
