Fichas
Sequences and Series
Fichas del conjunto (13)
- 1Name three types of sequenceArithmetic
Geometric
Fibonacci - 2What is an arithmetic sequenceAdds or subtracts a constant with each term
- 3What is the formula for the kth term of an arithmetic sequence\[a_k = a + (k - 1)d\]
- 4Define the following for an arithmetic sequence: 1. \(a\) 2. \(d\) 3. \(k\) or \(n\) 4. \(a_k\) 5. \(S_n\)1. The first term
2. The common difference
3. The term number
4. The kth term
5. The sum to n terms - 5What is the formula for the sum to n terms of an arithmetic sequence?\[S_n = \frac{n}{2}[2a + (n - 1)d]\]
- 6Prove the formula for the sum to n terms of an arithmetic sequence\(S_n = a + (a + d) + ... + [a + (n - 2)d] + [a + (n - 1) d]\)
\(S_n = [a + (n - 1)d] + [a + (n - 2)d] + ... + (a + d) + a\)
\(2S_n = n[2a + (n - 1)d]\)
\(S_n = \frac{n}{2}[2a + (n - 1)d]\) - 7What is a geometric sequence?Multiply or divide by a constant with each term
- 8Define the following 1. a 2. r 3. \(S_n\) 4. \(S_\infty\)1. First term
2. Common ratio
3. Sum to n terms
4. Sum to infinity - 9Formula for \(a_k\) in a geometric sequence\[a_k = ar^{k - 1}\]
- 10Formula for the sum to n terms of a geometric sequence\[S_n = \frac{a(1 - r^n)}{1 - r}\]
- 11Prove the formula for the sum to n terms of a geometric sequence\(S_n = a + ar + ar^2 ... + ar^{n - 2} + ar^{n - 1}\)
\(rS_n = ar + ar^2 + ... + ar^{n - 2} + ar^{n - 1} + ar^n\)
\(S_n - rS_n = a - ar^n\)
\(S_n(1 - r) = a(1 - r^n)\)
\(S_n = \frac{a(1 - r^n)}{1 - r}\) - 12What is the sum to infinity of a geometric sequence?\[S_\infty = \frac{a}{1 - r}\]
- 13When is the sum to infinity of a geometric sequence valid?\[\lvert r\rvert < 1\]
Información
- Descripción
- A level (Sequences and Functions) OCR A level Maths Fichas sobre Sequences and Series, creado por James Norman el 31/12/2018.
- Creado por
- James Norman
- Visitas
- 3
- Valoración