Y2, C3 - Sequences & Series Flashcards

1
Q

What is an arithmetic sequences

A

A sequence which has a common difference between the terms

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2
Q

What is a geometric sequence

A

A sequence which has a common ratio between the terms

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3
Q

What is a Fibonacci sequence

A

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

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4
Q

What does un denote in sequences

A

the nth term
u3 would be the 3rd term

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5
Q

What does n denote in sequences

A

The position of the term in the sequence

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6
Q

What does a denote in sequences

A

The first term

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7
Q

What does d denote in sequences

A

The difference between terms

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8
Q

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

A

un = a + (n - 1)d

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9
Q

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

A

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

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10
Q

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

A

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

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11
Q

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

A

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

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12
Q

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

A

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

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13
Q

What is an alternating sequence

A

A sequence which oscillates between positive and negative

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14
Q

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

A

un = ar^n-1

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15
Q

What does r denote in geometric sequences

A

The common ratio

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16
Q

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

A

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

17
Q

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

A

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

18
Q

When will an infinite series converge

A

When lrl < 1

19
Q

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

A

r^n –> 0

20
Q

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

A

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

21
Q

What is a recurrence relation

A

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

22
Q

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

A

The terms in the sequence repeat every 3

23
Q

How to solve most sigma equations

A

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

24
Q

What is a strictly increasing sequence

A

A sequence where the terms are always increasing

25
Q

What is a strictly decreasing sequence

A

A sequence where the terms are always decreasing

26
Q

What is a periodic sequence

A

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

27
Q

What is order k in a periodic sequence

A

How often the sequence repeats