Sequences And Series

Question 1

Equation for arithmetic sequences

Answer 1

uₙ = a + (n - 1)d

n = term
a = first term
d = common difference

Question 2

Equation for geometric sequences and series

Answer 2

uₙ = ar^(n - 1)

n = term
a = first term
r = common ratio

Question 3

Equation for arithmetic series

Answer 3

Sₙ = n/2(2a + (n - 1)d)

a = first term
d = common difference

Can also be written as
Sₙ = n/2(a + l)

l = last term

Question 4

What other equation can we use to find the common ratio, r, in a geometric sequence or series?

Answer 4

u2/u1 = u3/u2 = u4/u3 etc

Question 5

Equation for geometric series

Answer 5

Sₙ = (a - ar^n)/(1- r)

Question 6

Equation for sum to infinity of a geometric series

Answer 6

Sum to infinity = a/(1 - r)

Question 7

What is the difference between arithmetic and geometric sequences?

Answer 7

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms