Sequences and series 1: Sequences

Question 1

Define sequence

Answer 1

is a set of numbers in a given order

Question 2

Types of sequences

Answer 2

• increasing
• decreasing
• arithmetic
• geometric
• periodic

Question 3

Describe increasing sequence

Answer 3

each term is greater than the one before

Question 4

Describe decreasing sequence

Answer 4

each term is less than the one before

Question 5

Describe arithmetic sequence

Answer 5

the difference between one term and the next is always the same

Question 6

Describe geometric sequence

Answer 6

the ratio of one term to the next is always the same

Question 7

Describe periodic sequence

Answer 7

• repeats itself at regular intervals
• the no. of terms before the sequence repeats is called the period

Question 8

Define series

Answer 8

• the sum of the terms of a sequence
• notation for this is the greek symbol Σ (sigma)

Question 9

Describe sequences defined deductively

Answer 9

• a deductive definition gives a direct formula for the kth term of the sequence in terms of k
• terms of the sequence can be found by substituting the numbers 1,2,3… for k

Question 10

Describe sequences defined inductively

Answer 10

• an inductive definition tells you how to find a term in a sequence from the previous term
• must also include the value of the first term of the sequence

Question 11

Formulas you need to know for arithmetic sequences

Answer 11

kth term of a sequence:
ak = a + (k-1)d
Sum of the first n terms:
Sn = 1/2 n [2a + (n-1)d]
where a is the first term
where d is the common difference

Question 12

Formulas you need to know for geometric sequences

Answer 12

kth term of a sequence:
ak = ar^k-1
Sum:
Sn = a(1-r^n) / 1 - r
Sum to infinity:
S∞ = a / 1-r for -1< r <1