further maths all algebra

what do we use to expand binomials

pascals triangle

pascals triangle

.

how to use pascals triangle to binomially expand

those numbers become the coefficients u use

where do the indices come from in binomial expansion

the main number in the bracket

then u do all the number bonds both ways

what is a quadratic sequence

second differences are constant

what is the nth term formula of a quadratic sequence

a quadratic equation

an² + bn + c

how to find the a from an² + bn + c

1. find second difference

2. divide it by 2

how to find b and c from an² + bn + c

1. write out first 3 or 4 terms of the an² that you found

2. write out the corresponding terms of the given sequence under

3. find the difference between each pair of numbers

4. find the linear nth term of these differences

5. this is bn + c

what is a limiting value

the number a sequence gets closer and closer to but never reaches

limiting value

(inc when n is a power)

0

because the fraction gets smaller and smaller

limiting value

also 0

keeps getting smaller

nth term formulae that are algebraic fractions - limiting value

divide every term (top and bottom) by highest power of n

(see picture)

5n limiting value

no limiting value

not all sequences have one

graph type

increasing

graph type

decreasing

graph type

decreasing

because the base number is between 0 and 1

graph type

increasing

because the base number is between 0 and 1

y intercept of this type of graph (and the one with a negative x)

(0,a)

because if u sub 0 into the x its just 1xa

do exponential graphs cross the x axis

no

do exponential graphs have minimum or maximum points

no they are always increasing or decreasing

how to find equation of exponential graph

sub in the y and x coordinates into the equation theyve given you to find unknown constants