Arithmetic Sequences Using Recursion (VCE SSCE General Mathematics): Flashcards

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Arithmetic Sequences Using Recursion
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Recurrence relation (two parts)

Starting value + rule for finding next term

General form of recurrence relation

t0=a,tn+1=tn+Dt_0 = a, t_{n+1} = t_n + D

aa in tn=a+nDt_n = a + nD

Starting value (initial term)

DD in tn=a+nDt_n = a + nD

Common difference

Direct formula for nth term

tn=a+nDt_n = a + nD

nn in tn=a+nDt_n = a + nD

Term number (0, 1, 2, 3...)

Positive DD in arithmetic sequence

Sequence increases

Negative DD in arithmetic sequence

Sequence decreases

Common difference in tn+1=tn2t_{n+1} = t_n - 2

D=2D = -2

t0t_0 notation meaning

First term of sequence

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