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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!)


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