Topic 3 Sequences and series

Question 1

What is a sequence

Answer 1

Items of a pattern listed in order

Question 2

What is a term

Answer 2

An individual number in a sequence

Question 3

What is a series

Answer 3

All the terms in a sequences added together

Question 4

What is an arithmetic sequence

Answer 4

A sequence in which by the next term is determined by adding or subtracting a fixed amount

Question 5

In arithmetic sequences, what does the letter d denote

Answer 5

Common difference

Question 6

In arithmetic sequences, what does the letter a denote

Answer 6

The first term

Question 7

What’s the formula for the nth term of an arithmetic sequence

Answer 7

Un = a + (n-1)d

Question 8

What is the formula for the sum of the first n terms of an arithmetic series

Answer 8

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

Question 9

What is the formula for the nth term of a geometic sequence

Answer 9

Un = ar^n-1

Question 10

What is the formula for the sum of the first n terms of a geometric series

Answer 10

a(1-r^n) / 1-r

Question 11

For a geometric series to have a sum to infinity, is the modulus of r greater or smaller than one and what is the name for this

Answer 11

Modulus of r is smaller than one so the series is convergent