Sequence Flashcards
What is a sequence?
An ordered list of numbers
What is an arithmetic sequence?
Take each term, and add the same amount to it
+ 3 , + 3, + 3
4, 7, 10, 13 …
common difference = 3
What is a geometric sequence
multiply each term by the same amount
x 3 , x 3, x3,
4, 12, 36, 108 ….
no common difference here but we have a common ratio of 3
a1 = 4 a3 = 10 a39 = ?
????
48, 20, 6, -1
In the sequence above, each term after the first is found by dividing the previous term by a and subtracting b from that result. What is the value of b - a ?
guess and check
a = 2 b = 4
b - a = 4 - 2 = 2
answer = 2
What is the first thing you do in a patterns and sequences question?
Write out the terms until you see a pattern, start from the beginning
What is the second thing you do in a patterns and sequences question?
If you see something that would be impossible to calculate, look for a pattern
What is the third thing to try in a sequences question?
plug in the answers if the question asks for the value of a specific term, such as the first term
What is the units digit to 3^333 ?
Answer = 3
The units digit of any number will be of the product of a multiplication problem will be the units digit of what the first thing is times 3
333 / 4(because 4 numbers in the cycle) = 83 with a remainder of 1
3^1 = 3 (which is remainder 1) 3^2 = 9 (remainder 2) 3^3 = 27 (remainder 3) 3^4 = 81 (remainder 4) 3^5 = 243 (remainder 1) 3^6 = 729 (remainder 2)
If you have a set of numbers that is evenly spaced, then the average is equal to the ?
median
the function f is defined by f((x + 14) / (4)) = 5x^2 - 2x + 10 for all numbers x. What is the value of f(5) ?
First thing you do is set ((x + 14) / 4) = 5 then solve.
When you solve you get x = 6 THEN you put x = 6 into
the equation 5x^2 - 2x + 10 to get = 178 which is the answer.
