Arithmetic Sequences:
2, 4, 6, 8 --> n + 2 (this is referred to as a common difference or d)
The common difference can be determined by subtracting a(2) from a(1).
The Formula of Arithmetic Sequences: a(n) = a(1) + (n - 1)d (explicit formula)
2, 4, 6, 8: a(n) = 2 + (n - 1)2
a(n) = 2 + 2n - 2
a(n) = 2n
The Formula of the Sum of Arithmetic Sequences: S(n) = n/2 (a(1) + a(2))
S(100) = 100/2 (2 + 2(100))
S(100) = 50 (202)
S(100) = 10,100
Reclusive Formulas:
A reclusive formula must always include 2 parts:
The first part indicates where the sequence starts and the second part indicates the direction of the sequence, for instance, whether you add or subtract.
a(k+1) = a(k) + 1 OR a(k) = a(k-1) + 1
a(1) = 3
a(2) = 3 + 1 = 4
a(3) = 4 + 1 = 5
a(4) = 5 + 1 = 6
According to the formula provided, you would add 1 to the preceding term every time you wish to find the next term. For instance, to find the second term, you would add 1 to the first term, and so forth.
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