Number Sequence

For number sequences formulas:

A. Common difference:

nth term = a + (n - 1)d

d is difference between the numbers

a is first term

n is the nth term - leave it there.

Eg formula for this number pattern: 5, 8, 11, 14, 17, 20...

a = 5

d = 3

therefore, formula is:

5 + (n - 1)(3)

simplify ---> 5 + 3n - 3 = 2 + 3n (ans)

B. Changing difference:

nth term = a + (n - 1)d + ½(n - 1)(n - 2)c

a is first term

d is first difference

c is difference of the difference

n is the nth term - leave it there

Eg Formula for this number pattern: 6, 8, 12, 18, 26...

difference between each subsequent number is 2, 4, 6, 8...

a = 6

d = 2

c = 2

therefore, formula is: 6 + (2)(n-1) + 2/2(n - 1)(n - 2)

Simplify ---> 6 + 2n - 2 + 1(n² - 2n - n + 2)

= 6 + 2n - 2 + n² - 2n - n + 2

= 6 - n + n² (ans)

^{(test the answers yourself!)}