Sequences and series

Question 1

What is a sequence?

Answer 1

A series of numbers following a set rule

Question 2

What is a term in a sequence?

Answer 2

The value at a specific location

Question 3

How is the nth term of a sequence notated?

Answer 3

Uⁿ

Question 4

What is a recurrence relation?

Answer 4

A way of defining a sequence in which initial values are given, and then each term is calculated from one or more previous term(s), i.e. Uⁿ⁺¹=2Uⁿ

Question 5

What is an arithmetic sequence?

Answer 5

A sequence in which the difference between two successive terms is constant

Question 6

What is a series?

Answer 6

The sum of a finite or infinite number of terms of a sequence

Question 7

How can the nth term of an arithmetic sequence be calculated, given the first term (a) and the common difference (d)?

Answer 7

a+d(n-1)

Question 8

How is the sum of the first n terms of a sequence notated?

Answer 8

Sⁿ

Question 9

How can Sⁿ be calculated, given the first term (a) and the common difference (d)?

Answer 9

(n/2)(2a+d(n-1))

Question 10

How can Sⁿ be calculated, given the first term (a) and the nth term (L)?

Answer 10

(n/2)(a+L)

Question 11

Describe sigma notation

Answer 11

“Σf(r), r=a to b” means to go through all integers between a and b (inclusive) and add f(r) to the running total