Sequences and series day 1-4 key equations

5/10/24

aₙ = a₁ + d(n-1)

explicit formula

the common difference between terms in an arithmetic sequence

What does d represent?

d = aₙ - aₙ-₁

arithmetic d equation

slope

what else is d equal to? (comes from subtracting y and y and x and x from two points)

Sₙ = n/2 (a₁ + aₙ)

arithmetic sum equation

n=1 on bottom, last n on top, and aₙ in middle of ∑

sigma notation

given a₁ = #, aₙ = aₙ-₁ + d

recursive formula (2 pts)

the recursive formula is a formula that relies on knowing the previous slot value

the recursive formula is a formula that relies on knowing the previous slot value

tₙ = tₙ-₁ + tₙ-₂

Fibonacci sequence formula

tₙ = n / n+1

arithmetic formula for fractions

“arithmetic means” refer to any terms in an arithmetic sequence that lie between two non-consecutive terms

“arithmetic means” refer to any terms in an arithmetic sequence that lie between two non-consecutive terms