Summary (Grade 12 NSC Matric Mathematics): Flashcards

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Arithmetic sequence definition

Sequence with constant difference between consecutive terms

Nth term formula for arithmetic sequence

Tn=a+(n−1)dT_n = a + (n - 1)d

Quadratic sequence definition

Sequence where second differences are constant

General formula for quadratic sequence

Tn=an2+bn+cT_n = an^2 + bn + c

Geometric sequence definition

Sequence with constant ratio between consecutive terms

Nth term formula for geometric sequence

Tn=arn−1T_n = ar^{n-1}

Arithmetic series sum with first and last term

Sn=n2[a+l]S_n = \frac{n}{2}[a + l]

Geometric series sum formula when r<1r < 1

Sn=a(1−rn)1−rS_n = \frac{a(1 - r^n)}{1 - r}

Sum to infinity formula for geometric series

S∞=a1−rS_\infty = \frac{a}{1 - r}

Condition for sum to infinity to exist

−1<r<1-1 < r < 1

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