Sequences and Series

Question 1

Binomial Expansion

Answer 1

Remember to sub (bx)

Question 2

Valditiy

Answer 2

-1 < bx < 1
Equivilent to
|bx| < 1

Question 3

Weird looking fraction

Answer 3

Split into partial fractions

Question 4

Fractional all to the same power

Answer 4

Numberator power
Denominator -power

Question 5

Approximating

Answer 5

Set value = a + bx
Solve for x and sub in
If X out of range
Factor out value

Question 6

Arithmetic Sequence nth term

Answer 6

a + (n-1)d

Question 7

Arithmetic Series

Answer 7

Sum of all terms

Question 8

Derive arithmetic series

Answer 8

Write out sum:
(a) + (a + d) + (a + 2d) + … + a+ (n-1)d

Write in reverse order

Add together to get
(2a + (n - 1)d) * n

Divide by 2

Question 9

nth term

Answer 9

ar^n-1

Question 10

Terms in geometric sequence

Answer 10

Use simultaneous equations

Question 11

What is the general term

Answer 11

Nth term

Question 12

term-to-term

Answer 12

position-to-term

Question 13

Sigma Notation

Answer 13

Sigma means sum

Top number - upper number
Bottom number - lower number
f(r), do this for each number and add together

Question 14

Recurrence relations

Answer 14

Un+1 = f(Un)

Question 15

Recurrence summations

Answer 15

Arithmetic: Identify a and d
Geometric: Identify a and r

Question 16

Modelling:

Answer 16

Finance based
If a quantity is repeatedly changing