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