Y2, C3 - Sequences & Series

Question 1

What is an arithmetic sequences

Answer 1

A sequence which has a common difference between the terms

Question 2

What is a geometric sequence

Answer 2

A sequence which has a common ratio between the terms

Question 3

What is a Fibonacci sequence

Answer 3

A sequence where each term is the previous two terms added together

Question 4

What does un denote in sequences

Answer 4

the nth term
u3 would be the 3rd term

Question 5

What does n denote in sequences

Answer 5

The position of the term in the sequence

Question 6

What does a denote in sequences

Answer 6

The first term

Question 7

What does d denote in sequences

Answer 7

The difference between terms

Question 8

What is the formula for the nth tern of an arithmetic sequence

Answer 8

un = a + (n - 1)d

Question 9

For which values of x would the expression -8, x^2, 17x form the first 3 terms of an arithmetic sequence

Answer 9

Find d (difference)
x^2 - -8 = 17x - x^2
2x^2 - 17x + 8 =0
x = 8, 0.5

Question 10

What is the formula for the sum of n terms of an arithmetic sequence (formula booklet)

Answer 10

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

Question 11

What is the alternative formula for the sum of n terms in an arithmetic sequence using the last term (L) (formula booklet)

Answer 11

Sn = (n/2) (a + L)

Question 12

Find the minimum number of terms for the sum 4 + 9 + 14 + … to exceed 2000

Answer 12

Use formula Sn = (n/2)(2a + (n-1)d)
d = 5, a = 4
4000 < n (8 + 5n - 5)
n = 27.99 therefore n = 28

Question 13

What is an alternating sequence

Answer 13

A sequence which oscillates between positive and negative

Question 14

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

Answer 14

un = ar^n-1

Question 15

What does r denote in geometric sequences

Answer 15

The common ratio

Question 16

The numbers 3, x, x+6 form the first 3 terms of a +ve geometric sequence, find x

Answer 16

Use formula ar^n-1
(x / 3) must equal ((x + 6) / x )
Therefore x = -3 or 6
As sequence +ve, x = 6

Question 17

What is the formula for the first n terms of a geometric sequence

Answer 17

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

Question 18

When will an infinite series converge

Answer 18

When lrl < 1

Question 19

If lrl < 1, what happens as r^n tends to infinity

Answer 19

r^n –> 0

Question 20

What is the formula for the sum to infinity of a convergent geometric series

Answer 20

S(infinity) = a / (1 - r)

Question 21

What is a recurrence relation

Answer 21

A term-to-term sequence
The formula tells you the next term in relation to another term e.g.
u(n+1) = 2u(n) + 4

Question 22

What does it mean if a recurrence relation sequence has a periodic order of 3

Answer 22

The terms in the sequence repeat every 3

Question 23

How to solve most sigma equations

Answer 23

Sub in first few / last few values and look for patterns

Question 24

What is a strictly increasing sequence

Answer 24

A sequence where the terms are always increasing

Question 25

What is a strictly decreasing sequence

Answer 25

A sequence where the terms are always decreasing

Question 26

What is a periodic sequence

Answer 26

A sequence where the terms repeat in a cycle of order k

Question 27

What is order k in a periodic sequence

Answer 27

How often the sequence repeats