> See also: > - [[Sequences]] > - [[Sums and Series]] # Sequences and Series ![[Pasted image 20230309013509.png|600]] ## Arithmetic Sequences/Series **Arithmetic Sequences:** When you add the same thing over and over. - Recursive Formula: $A(n)=A(n-1)+d$ - Explicit Formula: $A(n)=A(1)+d(n-1)$ $a_n = a_1 + (n-1)d$ $a_j = a_i + (j-i)d$ $S_n = \frac{(a_1 + a_n)n}{2}$ - $a_1$ = the first term - $d$ = the common difference - $n$ = the number of terms ## Geometric Sequences **Geometric Sequences:** When you multiply the same value over and over. - Recursive Formula: $A_n=A_{n-1} \cdot r$ - Explicit Formula: $A_n=a_1 \cdot r^{n-1}$ ## Harmonic Sequences ## Recursive Sequences > See also: > - [[Recursion]] ### The Fibonacci Sequence - What about recursive series? Do they also exist? tags: --- > See also: > - [[Sequences (Math)]] > - [[Sums and Series]] # Sequences and Series ![[Pasted image 20230309013509.png|600]] ## Arithmetic Sequences/Series **Arithmetic Sequences:** When you add the same thing over and over. - Recursive Formula: $A(n)=A(n-1)+d$ - Explicit Formula: $A(n)=A(1)+d(n-1)$ $a_n = a_1 + (n-1)d$ $a_j = a_i + (j-i)d$ $S_n = \frac{(a_1 + a_n)n}{2}$ - $a_1$ = the first term - $d$ = the common difference - $n$ = the number of terms ## Geometric Sequences **Geometric Sequences:** When you multiply the same value over and over. - Recursive Formula: $A_n=A_{n-1} \cdot r$ - Explicit Formula: $A_n=a_1 \cdot r^{n-1}$ ## Harmonic Sequences ## Recursive Sequences > See also: > - [[Recursion]] ### The Fibonacci Sequence - What about recursive series? Do they also exist?