Sequences and Series

Question 1

what is an arithmetic/ linear sequence

Answer 1

• adding on a set value every time e.g. 2, 5, 7

Question 2

what is a geometric sequence

Answer 2

• when a multiple is applied to it e.g. 1, 6, 36

- the number of the multiple used each time is called the ratio

Question 3

what is a converging sequence

Answer 3

• when the sequence is narrowing down to a single value e.g. 1/2, 1/4, 1/8, 1/16

Question 4

what is a diverging sequence

Answer 4

• when the sequence is ever growing – only getting larger and further apart e.g. 1, 4, 9, 16

Question 5

what is the U1 in a sequence

Answer 5

• the first term in the sequence

Question 6

what is the Un in a sequence

Answer 6

• the nth term

Question 7

Sn for geometric sequences formula

Answer 7

a(1 - rⁿ) / 1 - r

Question 8

what is the nth term for geometric sequences

[deductive definition]

Answer 8

Un =a x rⁿ⁻¹
a1 = first term in the sequence
r = common ratio
n = term number

Question 9

Sum to infinity formula

[geometric sequences]

Answer 9

S∞ = a1 / (1-r )

Question 10

Sn for arithmetic sequences formula

Answer 10

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

Question 11

what is the inductive formula for a geometric sequence

Answer 11

A(n+1) = r x An
A (only written like this because i can’t get subscript) = first term
r = common ratio
n = no. of terms

Question 12

arithmetic sequence formula

[gives you the nᵗᵸ term)

Answer 12

Un = a + (n-1)d

Question 13

how to find the first term when you are given teo terms in a geometric sequence

Answer 13

• substitute the values into the equation Un =a x rⁿ⁻¹
• then make the values equal to each other
• solve

Question 14

what is the name for geometric sequences that tend towards a particular value

Answer 14

• converging sequences

Question 15

what is the name for geometric sequences that become further and further away from their starting point

Answer 15

• diverging sequences

Question 16

formula for the sum of natural numbers

Answer 16

Sn = 1/2 n(n + 1)