Math formulas: Arithmetic and geometric Series


0 formulas included in custom cheat sheet

Number of terms in the series: $n$

First term: $a_1$

$N^{th}$ term: $a_n$

Sum of the first $n$ terms: $S_n$

Difference between successive terms: $d$

Common ratio: $q$

Sum to infinity: $S$

$$ a_n = a_1 + (n-1)d $$

$$ a_i = \frac{a_{i-1} + a_{i+1}}{2} $$

$$ S_n = \frac{a_1 + a_n}{2} \cdot n $$

$$ S_n = \frac{2 \cdot a_1 + (n-1) \cdot d}{2} \cdot n $$

$$ a_n = a_1 \cdot q^{n-1} $$

$$ a_i = \sqrt{a_{i-1} \cdot a_{i+1}} $$

$$ S_n = \frac{a_nq - a_1}{q-1} $$

$$ S_n = \frac{a_1 \cdot \left(q^n - 1 \right)}{q-1} $$

$$ S = \frac{a_1}{1-q}, \quad (\text{for } -1 < q < 1)$$

Algebra formulas

Creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.

Eric Temple Bell

Please tell me how can I make this better.