Notation:
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
Arithmetic Series Formulas:
\( a_n = a_1 + (n-1)d \)
\( a_i = \frac{a_{i-1} + a_{i+1}}{2} \)
\( S_n = \frac{a_1 + a_n}{2} \cdot n \)
\( S_n = \frac{2 \cdot a_1 + (n-1) \cdot d}{2} \cdot n \)
Geometric Series Formulas:
\( a_n = a_1 \cdot q^{n-1} \)
\( a_i = \sqrt{a_{i-1} \cdot a_{i+1}} \)
\( S_n = \frac{a_nq – a_1}{q-1} \)
\( S_n = \frac{a_1 \cdot \left(q^n – 1 \right)}{q-1} \)
\( S = \frac{a_1}{1-q}, \quad (\text{for } -1 < q < 1) \)