SEQUENCES AND SERIES
SEQUENCES
ARITHMETIC SEQUENCES:
An arithmetic (or linear) sequence is an ordered set of numbers (called terms) in
which each new term is calculated by adding a constant value to the previous
term.
The general term for an arithmetic sequence:
Tn = a+(n−1)d
Where:
• a = first term
• d = common difference
• n = is the position of the term in the sequence
• Tn = is the nth term
Test for an arithmetic sequence
To test whether a sequence is an arithmetic sequence or not, check if the
difference between any two consecutive terms is constant:
d = T2−T1 = T3−T2 = … = Tn−Tn−1
If this is not true, then the sequence is not an arithmetic sequence.
QUADRATIC SEQUENCES:
A quadratic sequence is a sequence of numbers in which the second difference
between any two consecutive terms is constant.
The general formula for the term of a quadratic sequence is:
𝑇𝑛 = 𝑎𝑛% + 𝑏𝑛 + 𝑐
It is important to note that the first differences of a quadratic sequence form an
arithmetic sequence. This sequence has a common difference of 2a between
SASHTI NOTES 1
SEQUENCES
ARITHMETIC SEQUENCES:
An arithmetic (or linear) sequence is an ordered set of numbers (called terms) in
which each new term is calculated by adding a constant value to the previous
term.
The general term for an arithmetic sequence:
Tn = a+(n−1)d
Where:
• a = first term
• d = common difference
• n = is the position of the term in the sequence
• Tn = is the nth term
Test for an arithmetic sequence
To test whether a sequence is an arithmetic sequence or not, check if the
difference between any two consecutive terms is constant:
d = T2−T1 = T3−T2 = … = Tn−Tn−1
If this is not true, then the sequence is not an arithmetic sequence.
QUADRATIC SEQUENCES:
A quadratic sequence is a sequence of numbers in which the second difference
between any two consecutive terms is constant.
The general formula for the term of a quadratic sequence is:
𝑇𝑛 = 𝑎𝑛% + 𝑏𝑛 + 𝑐
It is important to note that the first differences of a quadratic sequence form an
arithmetic sequence. This sequence has a common difference of 2a between
SASHTI NOTES 1
