PRECALCULUS 11: Sequences & Series (TERMS)

935 (literally ripped from angie's doc but if you like flashcards, use this)

Sequence

It is a list of items in a specific order. This can be classified by the number of terms: infinite and finite, or by pattern: arithmetic, geometric, harmonic, and fibonacci.

Infinite Sequence

It is a sequence that contains a countless number of terms. The ellipsis (...) located at the end of the sequence shows that the sequence is infinite. (e.g. 1,3,5,7,9…)

Finite Sequence

It is a sequence that contains a limited number of terms. This means that the last term of the sequence is known. (e.g. 1,3,5,7,9)

Series

The sum of the terms of a sequence.

Arithmetic Sequence

 It is a sequence of numbers in which each term after the first (a₁) is obtained by adding a constant number. This constant is called the common difference (d). (e.g. 4,7,10,13,16,19)

aₙ = a₁ + (n - 1)d

Formula for finding the nth term (aₙ) of a arithmetic sequence

aₙ = dn + c

• Formula for finding the nth term of an arithmetic sequence when you are not given the first term but are given the common difference
  

• Mainly for the simplified linear form of the formula when n is not given

Arithmetic Series/Summation/Sum

It is the total obtained by adding all the terms of an arithmetic sequence, where each term increases or decreases by a constant difference.

Sₙ = n/2 [2a₁ + (n − 1)d]

Formula for Arithmetic Series

n(a₁+aₙ)/2

Formula for Arithmetic Series given aₙ

Geometric Sequence

It is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a constant number. This constant is called the common ratio.

aₙ = a₁ · rⁿ ⁻ ¹

Formula for Geometric Sequence

Geometric Series

It is the total obtained by adding all the terms of a geometric sequence, where each term is multiplied by a constant ratio to get the next term.

Sₙ = a₁(1 - rⁿ) / (1 - r)

Formula for Geometric Series