A2 Sequences and Series

Question 1

Periodic Sequence

Answer 1

• A sequence which repeats itself at regular intervals.
• The number of terms before the sequence repeats is called the period.

Question 2

Arithmetic Sequence

Answer 2

A sequence with the same different between each term, can be positive or negative.

Question 3

Geometric Sequence

Answer 3

A sequence that has the same ratio between each term and the previous term.

Question 4

What is a deductive sequence?

Answer 4

A sequence which gives a direct formula for working out each term of the sequence, e.g. Ak = 2k + 1

Question 5

What is an inductive sequence?

Answer 5

A sequence which tells you how to find each term from the previous one, e.g. Ak+1 = Ak - 3

Question 6

What is the nth term of an arithmetic sequence?

Answer 6

a + (n-1)d;
where a is the first term, d is the common difference

Question 7

Formula for the sum of the first n terms of an arithmetic sequence, Sn

Answer 7

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

Question 8

Formula for the sum of the first n terms of an arithmetic sequence, Sn, expressed with the last term L

Answer 8

Sn = n/2 (a + L)
a = first term
L = last term

Question 9

Formula for the sum of the first n natural numbers

Answer 9

n (n+1) / 2

Question 10

Formula for the nth term of a geometric sequence

Answer 10

ar^(n-1)
a = first term
r = ratio

Question 11

Formula for the sum of the first n terms of an geometric sequence, Sn, to use when r < 1

Answer 11

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

Question 12

Formula for the sum of the first n terms of an geometric sequence, Sn, to use when r > 1

Answer 12

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

Question 13

For what values of r is a geometric sequence considered convergent? How do you write this?

Answer 13

-1 < r < 1
r^n will get closer to zero as n increases

lim r^n = 0
n –> ∞

Question 14

Formula for the sum to infinity of a convergent geometric sequence sequence

Answer 14

S∞ = a / 1 - r