- Messages
- 1,767
- Reaction score
- 22,887
- Points
- 523
Fatima18 I found it!! 
When a sequence of numbers is given, ex:
3, 6,9,12,…
Find the difference. In this case, the difference between 3 and 6 is 3. The difference between 6 and 9 is 3, so we use "an + b" to find the formula. Using this, we have to form 2 possible formulas.
When n=1, and when n=2 (you can also form a formula when n=3, or 4, but I used when n=1, and 2)
In this case, when n=1, the formula is a+b=3
When n=2, the formula is 2a+b=6
Using elimination method or substitution method, find a and b. you then have the formula for the nth term.
If the difference between the numbers is not the same, ex: if the difference between the first and second is 1, n the difference between the second and third is 2, den we use "an^2 + bn + c"
Ex: if the sequence is 2,6,12,20,30,…
The difference between the first and second number is 4, the difference between the second number and the third number is 6, and the difference between the third number and the fourth number is 8. These differences arr not the same, so we find the difference of these numbers. The difference between 4 and 6 is 2, and the difference between 6 and 8 is 2, so we use "an^2+bn+c".We have to form 3 equations because we have to find the values of a, b and c.
When n=1, a+b+c=2
When n=2, 4a+2b+c=6
When n=3, 9a+3b+c=12
First use 2 of the equations:
The second minus the first will form: 3a+b=4
The third minus the second will form: 5a+b=6
(you can choose which of the equations you want to use to form the second set of equations. It doesn't necessarily have to be the second minus the first, and the third minus the second. It can also be the third minus the first, or any other way)
Find a and b using the newly formed equations, then substitute those values in one of the main equations to find the value of c. You now have the equation for the nth term of dis sequence.
Hope this has helped you!!!
When a sequence of numbers is given, ex:
3, 6,9,12,…
Find the difference. In this case, the difference between 3 and 6 is 3. The difference between 6 and 9 is 3, so we use "an + b" to find the formula. Using this, we have to form 2 possible formulas.
When n=1, and when n=2 (you can also form a formula when n=3, or 4, but I used when n=1, and 2)
In this case, when n=1, the formula is a+b=3
When n=2, the formula is 2a+b=6
Using elimination method or substitution method, find a and b. you then have the formula for the nth term.
If the difference between the numbers is not the same, ex: if the difference between the first and second is 1, n the difference between the second and third is 2, den we use "an^2 + bn + c"
Ex: if the sequence is 2,6,12,20,30,…
The difference between the first and second number is 4, the difference between the second number and the third number is 6, and the difference between the third number and the fourth number is 8. These differences arr not the same, so we find the difference of these numbers. The difference between 4 and 6 is 2, and the difference between 6 and 8 is 2, so we use "an^2+bn+c".We have to form 3 equations because we have to find the values of a, b and c.
When n=1, a+b+c=2
When n=2, 4a+2b+c=6
When n=3, 9a+3b+c=12
First use 2 of the equations:
The second minus the first will form: 3a+b=4
The third minus the second will form: 5a+b=6
(you can choose which of the equations you want to use to form the second set of equations. It doesn't necessarily have to be the second minus the first, and the third minus the second. It can also be the third minus the first, or any other way)
Find a and b using the newly formed equations, then substitute those values in one of the main equations to find the value of c. You now have the equation for the nth term of dis sequence.
Hope this has helped you!!!
