Constant Difference Sequences
This is when the difference between terms is always the same.
e.g. 1, 4, 7, 10
This has a difference which is always 3.
You can always find the 'nth term' by using this formula:
nth term = dn + (a - d)
Where d is the difference between the terms, a is the first term and n is the term number.
for eg lets find the 3rd term.. 3x3+(1-3) = 7
Changing Difference Sequences
2 , 3 , 6 , 11 , 18
1st dif. 1 3 5 7
diff of diff 2 2 2
Using the formula, nth term = a + (n - 1)d + ½(n - 1)(n - 2)c
This time there is a letter c which stands for the second difference (or the difference between the differences and d is just the difference between the first two numbers and a is the first term.
now for eg lets fine the 3rd term. 2+ (3-1)x1 + 0.5x(3-1)(3-2)x2 = 6
Hope this helped.
This is when the difference between terms is always the same.
e.g. 1, 4, 7, 10
This has a difference which is always 3.
You can always find the 'nth term' by using this formula:
nth term = dn + (a - d)
Where d is the difference between the terms, a is the first term and n is the term number.
for eg lets find the 3rd term.. 3x3+(1-3) = 7
Changing Difference Sequences
2 , 3 , 6 , 11 , 18
1st dif. 1 3 5 7
diff of diff 2 2 2
Using the formula, nth term = a + (n - 1)d + ½(n - 1)(n - 2)c
This time there is a letter c which stands for the second difference (or the difference between the differences and d is just the difference between the first two numbers and a is the first term.
now for eg lets fine the 3rd term. 2+ (3-1)x1 + 0.5x(3-1)(3-2)x2 = 6
Hope this helped.
