sequences Flashcards
list the general formula for a straight line
y=mx+c
describe the formula for finding out the gradient
rise/run
change in x
x₂ - x₁
describe the formula for finding the midpoint between two points
( x₂ +x₁ ) ( y₁ + y₂ )
———– , ————-
2 2
describe the formula for finding the distance between two points
√( x₂ - x₁ )² + ( y₁ - y₂ ) ²
define a linear sequence
the difference between the terms is constant is only either plus or minus
define a geometric sequence
each term is produced by multiplying the pervious by the common ratio
define fibonacci sequence
each term is produced by adding the previous two
define quadratic sequence
terms that follow square numbers n²
describe the alternate formula for the nth term
nth term = a + ( n - 1 ) d
a = first term
d = common difference
e.g. 3rd term = a + 2d
describe the formula for quadratic sequences
an² + bn + c
find out the first difference in your sequence, and then using those new numbers find the second difference with them. the number is then halved and put in the form n².
then use this n² and substitute it for the numbers increasing by one, e.g. 1,2,3, etc.
then with your new terms, find out the common difference and find the nth term rule.
add your n² and nth term rule together to get your final answer.
describe the formula for finding the nth term in a geometric sequence
nth term = a x 𝑟ⁿ⁻¹
a = first term
𝑟 = common ratio
find out the common ratio between the terms first and substitute the common ratio and n. proceed with the formula and round it off after the hundredths.
describe the formula for finding missing numbers in geometric sequences
first find out the common ratio between the two numbers and find the difference of the positions of the terms.
e.g. -2, __, -18
the positions are 1 and 3 so the
difference is one term and the common
ratio between the two terms is x9.
in this instance where there is only one term difference, you can square root it and find the common ratio from there. then substitute and proceed with your equation as normal.
describe the formula for iterative sequences
Uₙ = n³ +/- d
Uₙ = uₙ-1 = ( n+1 )⁺ⁿ
first substitute the n in Uₙ and do the first term multiply by n-1 ; this only work with finding U₂.
the terms after this will use the previous term to substitute.
e.g. U₃ will use U₂ in the formula since its
uₙ-1.
then follow the nth term you were given and get your answer.
describe the alternate formula for the nth term in arithmetic sequences
nth term = a + ( n - 1 ) d
a = first term
d = common difference
first find the difference in the position of terms and correlate that to the difference in terms.
e.g. 4n = 31 and 15n = 71, the difference in
the position of terms is 11 and the
difference of terms is 40.
then take the difference and put it in nth term.
e.g. a + 10d
then divide the difference in terms by the common difference, difference/d.
e.g. 40/10 = d
using the first term multiply the d in that term
e.g. 4n = a + 3d, do 3 x d
after you find the answer to 3(d),
minus it from 4n and you have now
found a.
you have now found a and d so substitute that in your formula and answer the question.