SEQUENCES AND SERIES
- Kabelo Nchabeleng
Sequences are number patterns that follow a particular rule. The rule, T n,
is the nth term of the sequence in terms of the number n where n is an
element of natural numbers.
In grade 12 we will study:
1. Arithmetic and geometric sequences
2. Arithmetic and geometric series
3. Sigma notation
1.1. Terminology and definitions:
- Sequence: a list of terms, T1, T2…
- Series: a sum of terms in a sequence, T1 + T2…
- Arithmetic sequence: a sequence with a common first difference
(d)
- Quadratic sequence: a sequence with a common second
difference (2a)
- Geometric sequence: a sequence with a common ratio (r.)
- Convergence: the tendency/approach towards a particular value
- Divergence - the approach to positive or negative infinity
1.2. Symbols
n - number of terms in a sequence or series
Tn - the nth term of a sequence or series
Sn - the sum to n terms of a series
d - the common first difference in an arithmetic sequence or series
r - the common ratio in a geometric sequence or series
a - first term (T1) of a sequence or series
l - the last term of a sequence or series
Sinfinity - sum to infinity of a convergent geometric sequence
1.3. Arithmetic Sequences and Series. (Linear pattern)
- Kabelo Nchabeleng
Sequences are number patterns that follow a particular rule. The rule, T n,
is the nth term of the sequence in terms of the number n where n is an
element of natural numbers.
In grade 12 we will study:
1. Arithmetic and geometric sequences
2. Arithmetic and geometric series
3. Sigma notation
1.1. Terminology and definitions:
- Sequence: a list of terms, T1, T2…
- Series: a sum of terms in a sequence, T1 + T2…
- Arithmetic sequence: a sequence with a common first difference
(d)
- Quadratic sequence: a sequence with a common second
difference (2a)
- Geometric sequence: a sequence with a common ratio (r.)
- Convergence: the tendency/approach towards a particular value
- Divergence - the approach to positive or negative infinity
1.2. Symbols
n - number of terms in a sequence or series
Tn - the nth term of a sequence or series
Sn - the sum to n terms of a series
d - the common first difference in an arithmetic sequence or series
r - the common ratio in a geometric sequence or series
a - first term (T1) of a sequence or series
l - the last term of a sequence or series
Sinfinity - sum to infinity of a convergent geometric sequence
1.3. Arithmetic Sequences and Series. (Linear pattern)
