Chapter 20 - Sequences and Series (Pure) Flashcards

1
Q

what does Un mean?

A

Un is the nth term of a sequence

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2
Q

what’s an increasing function?

A

an increasing function is when each term is larger than the previous term

Uk+1 is bigger than Un

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3
Q

what is a decreasing function?

A

a decreasing sequence is when each term is smaller than the last

Uk+1 is less than Uk

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4
Q

what’s a periodic sequence?

A

a periodic sequence is when the terms repeat in a cycle

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5
Q

whats an arithmetic sequence?

A

adding or subtracting a fixed amount.

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6
Q

what’s an arithmetic sequence equation?

A

Un = a + (N-1)d

a is the first term
d is the amount added each time
n is the position of any term.

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7
Q

the arithmetic series sum of equation is found on the data sheet.

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

A

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

a= first term
n= is the position of the term
d= is the difference
l= is the last term

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8
Q

what does Σ mean?

A

Σ means the sum of

15
Σ (2n +3)
n=1

15 means the last n is 15 from 1 to 15

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9
Q

what are natural numbers ? what is the sum of them?

A

natural numbers are positive whole numbers i.e 1,2,3,4,5

Sn= 1/2 n (n+1)

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10
Q

what’s a geometric sequence? what’s the formula?

A

a geometric sequence is multiplication by a common constant r

Un = ar ^(n-1)

a= first term
r= common ratio

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11
Q

the sum of a geometric series equation is found on the data sheet, what do the symbols stand for?

Sn= a(1-rⁿ)/ 1-r

A

Sn= a(1-rⁿ)/ 1-r

a is the first term
r is the common ratio
n is the term number

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