Chapter 20 - Sequences and Series (Pure)

Question 1

what does Un mean?

Answer 1

Un is the nth term of a sequence

Question 2

what’s an increasing function?

Answer 2

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

Uk+1 is bigger than Un

Question 3

what is a decreasing function?

Answer 3

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

Uk+1 is less than Uk

Question 4

what’s a periodic sequence?

Answer 4

a periodic sequence is when the terms repeat in a cycle

Question 5

whats an arithmetic sequence?

Answer 5

adding or subtracting a fixed amount.

Question 6

what’s an arithmetic sequence equation?

Answer 6

Un = a + (N-1)d

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

Question 7

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)

Answer 7

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

Question 8

what does Σ mean?

Answer 8

Σ means the sum of

15
Σ (2n +3)
n=1

15 means the last n is 15 from 1 to 15

Question 9

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

Answer 9

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

Sn= 1/2 n (n+1)

Question 10

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

Answer 10

a geometric sequence is multiplication by a common constant r

Un = ar ^(n-1)

a= first term 
r= common ratio

Question 11

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

Answer 11

Sn= a(1-rⁿ)/ 1-r

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