MATHEMATICS 10
1.Arithmetic Sequences
• Definition
An arithmetic sequence is a sequence in which the difference between consecutive terms is
constant.
Example: 1, 4, 7, 10, ...
Common Difference (d) = 3
•Forming Sequences
Numbers leaving remainder r when divided by n:
Number = n × k + r
Example:
Numbers leaving remainder 1 when divided by 3:
3k + 1
Sequence: 1, 4, 7, 10, …
Important Terms
● a = First term
● d = Common difference
● n = Position of term
● an = nth term
• Nth Term Formula
an = a + (n − 1)d
Used to find any term in the sequence.
Finding First Term
a = an − (n − 1)d
• General Form of AP
a, a + d, a + 2d, a + 3d, ...
Checking Whether a Number is a Term
Subtract the first term from the given number.
Divide by d.
If the result is a whole number, the number belongs to the sequence.
Otherwise, it is not a term.
•Finding Position of a Term
n = ((an − a) / d) + 1
If n is a whole number, the number is a term of the sequence.
Key Exam Tips
✓ Difference between consecutive terms is always d.
✓ Difference between any two terms is a multiple of d.
1.Arithmetic Sequences
• Definition
An arithmetic sequence is a sequence in which the difference between consecutive terms is
constant.
Example: 1, 4, 7, 10, ...
Common Difference (d) = 3
•Forming Sequences
Numbers leaving remainder r when divided by n:
Number = n × k + r
Example:
Numbers leaving remainder 1 when divided by 3:
3k + 1
Sequence: 1, 4, 7, 10, …
Important Terms
● a = First term
● d = Common difference
● n = Position of term
● an = nth term
• Nth Term Formula
an = a + (n − 1)d
Used to find any term in the sequence.
Finding First Term
a = an − (n − 1)d
• General Form of AP
a, a + d, a + 2d, a + 3d, ...
Checking Whether a Number is a Term
Subtract the first term from the given number.
Divide by d.
If the result is a whole number, the number belongs to the sequence.
Otherwise, it is not a term.
•Finding Position of a Term
n = ((an − a) / d) + 1
If n is a whole number, the number is a term of the sequence.
Key Exam Tips
✓ Difference between consecutive terms is always d.
✓ Difference between any two terms is a multiple of d.
