Algebra 3-4 Formulas
An=a₁+(n-1)d
arithmetic sequence (add or subtract) a₁= initial value, d= common difference and n=number of terms
Sn=.5n(2a₁+[n-1]d)
arithmetic series (sum) a₁= initial value, d= common difference and n=number of terms
Sn=a₁(1-rⁿ)/(1-r)
geometric finite series (sum) a₁= initial value, r= common multiplier and n=number of terms
y=ab∧x
Exponential equation where a=initial value, b=growth rate,
y-y₁=m(x-x₁)
The equation of a line in point slope form where (x₁, y₁) is a point and m is the slope.
(y₂-y₁)/(x₂-x₁)
The equation to find slope from 2 points
y=a|x-h|+k
The equation used to move around the absolute value graph. a=stretch factor, (h,k)=vertex. H moves the graph from left to right, and k moves the graph up or down. The larger stretch factors decrease the graph's width and the smaller stretch factors increase it.
Log Rules
log (a/b)= log(a)-log(b) log (a)(b)= log(a) +log(b) logxⁿ=nlogx log1=0 ln1=0
Log n (A)=P
n^P=A used to rewrite logs. Pronounced "log nap"
Sn=a₁/(1-r)
geometric infinite series (sum) a₁= initial value, r= common multiplier and n=number of terms *Can only use if r<1
An=a₁(r)ⁿ⁻¹
geometric sequence (multiply or divide) a₁= initial value, r= common multiplier and n=number of terms
Function
a function has one output for every input. This can be tested with the vertical line test.
Exponent rules
(xⁿ)(x°)=xⁿ⁺° (xⁿ)/(x°)=xⁿ⁻° (xⁿ)°=xⁿ°
y=ae^kt
Continuous exponential growth where a=initial value, k=growth percentage either ±
∑
Perform a sum of the series. First look if the sequence is arithmetic or geometric then use the correct series equation
y=a(x-h)²+k
Vertex form of a parabola, (h, k) is the vertex, x=h is the axis of symmetry, and a is the stretch factor