Arithmetic and Geometric Sequences

Flashcards covering arithmetic and geometric sequences and series, including formulas and recursive definitions.

arc length

S = r theta

Arithmetic Sequence Formula

an = a1 + (n-1)d

Sum of Arithmetic Sequence

Sn = n* (a1 + an)/2

Arc Area

A = 1/2*r²*theta

Geometric Sequence Formula

an = a1 * r^(n-1)

Geometric Sum (Finite)

S = a * (1 - r^n) / (1 - r)

Geometric Sum (Infinite)

S = a / (1 - r) (for |r| < 1, infinite geometric series).

Arithmetic Recursive Formula

an = an-1 + d

Geometric Recursive Formula

an = r * an-1

tan asymptotes

pi/2

Cotangent asymptotes

pi

Volume of a sphere

4/3*pi*r³

Surface Area of a Sphere

4*pi*r²