Applications of APs and GPs (HSC SSCE Mathematics Advanced): Flashcards

Sequence: ordered list; Series: sum of terms

Sequence with constant difference between consecutive terms

The constant difference between consecutive terms

$T_n = a + (n-1)d$

$x = \frac{a + b}{2}$ (middle term is average)

Sequence with constant ratio between consecutive terms

The constant ratio between consecutive terms

$T_n = ar^{n-1}$

$x^2 = ab$ (middle term squared equals product)

When $|r| < 1$ (i.e., $-1 < r < 1$)