Flashcards · Maths · Functions, Sequences and Rates of Change
Geometric and Special Sequences
-
What is a geometric sequence?
A sequence where each term is found by multiplying by the same number.
-
What is the common ratio?
The number you multiply by each time.
-
How do you find the common ratio?
Divide a term by the one before it.
-
What is the common ratio of \(80, 40, 20, 10\)?
\(\dfrac{1}{2}\).
-
What happens if the ratio is negative?
The terms alternate between positive and negative.
-
What is the \(n\)th term of a geometric sequence?
\(a \times r^{n-1}\).
-
What is the 6th term of \(2, 4, 8, \ldots\)?
64.
-
What is a Fibonacci-type sequence?
Each term is the sum of the two terms before it.
-
What is the next term of \(1, 1, 2, 3, 5, 8\)?
13.
-
What are the square numbers?
\(1, 4, 9, 16, 25, \ldots\).
-
What are the cube numbers?
\(1, 8, 27, 64, \ldots\).
-
What are the triangular numbers?
\(1, 3, 6, 10, 15, \ldots\).
-
If the 2nd term is 6 and the 5th is 48, what is \(r^3\)?
8.
-
What is the ratio of \(2, 2\sqrt{3}, 6\)?
\(\sqrt{3}\).
-
How do you tell arithmetic from geometric?
Arithmetic adds a constant, geometric multiplies by a constant.
-
Which part of this topic is Higher tier?
Finding the ratio from two terms, and a surd ratio.