Sequences - [Pure 4].

Question 1

What is a sequence?

Answer 1

A chain of numbers following a rule.

Question 2

What is a series?

Answer 2

A sequence that gets added up.

Question 3

What is the expression for an increasing sequence?

Answer 3

u_n+1 > u_n.

Question 4

What is the expression for an decreasing sequence?

Answer 4

u_n+1 < u_n.

Question 5

What is the expression for an periodic sequence?

Answer 5

u_n+a= u_n

Question 6

Whats the difference between Divergent and Convergent Sequences?

Answer 6

• Divergent Sequences don’t tend towards a limit.
• Convergent Sequences do tend towards a limit.

Question 7

What letter do we replace all the u_n, u_n+1, u_n-1’s with?

Answer 7

L and then solve to find L.

Question 8

What letter does the sigma notation look like?

Answer 8

An E.
* S_n=ⁿΣ_r=1(u_r).

Question 9

What does this mean?
³Σ_n=1(u_n).

Answer 9

Add up all the u_n’s from n=1 to n=3 (e.g. u₁, u₂, u₃).

Question 10

What letter is used for the common difference in an Arithmetic Sequence?

Answer 10

d.

Question 11

What letter is used for the first term in an Arithmetic Sequence and a Geometric Sequence?

Answer 11

a.

Question 12

What is the equation for the n^th term of an Arithmetic Sequence?

(NOT Given in Formula Booklet!)

Answer 12

u_n = a + (n-1)d.

Question 13

What letter is used for the last term in an Arithmetic Sequence?

Answer 13

l.

Question 14

What are the 2 equations for the ‘Sum to the n^th term’ for Arithmetic Sequences?

(Given in Formula Booklet!)

Answer 14

S_n = 1/2(n)[a+l] = 1/2(n)[2a + (n-1)d].

Question 15

What letter is used for the common difference in a Geometric Sequence?

Answer 15

r.

Question 16

When is a geometric sequence divergent?

Answer 16

When |r| > 1.

(Sequence gets bigger).

Question 17

When is a geometric sequence convergent?

Answer 17

When |r| < 1.

(Sequence gets smaller).

Question 18

What is the equation for the n^th term of a Geometric Sequence?

(NOT Given in Formula Booklet!)

Answer 18

u_n = ar^n-1.

Question 19

What is the equation for the Sum of the first ‘n’ terms of a Geometric Sequence?

(Given in Formula Booklet!)

Answer 19

S_n = a(1-rⁿ) / 1-r.

Question 20

What is the equation for the Sum to infinity of a Geometric Sequence when |r| < 1?

(Given in Formula Booklet!)

Answer 20

S_∞ = a / 1-r.