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Class 11 Math Sequences and Series Notes PDF
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Key Points Sequences and Series
• Sequence
A succession of numbers arranged in a definite order according to a given certain rule is called sequence.
• Finite sequence
Sequence having finite number of terms.
• Infinite sequence
Sequence having infinite number of terms.
• Progression
A sequence whose terms follow certain patterns are called progression.
• Series
If a₁, a₂, a₃, … an is a sequence, then the expression
a₁ + a₂ + a₃ + a₄ + …… + an is called series.
Arithmetic Progression (A.P)
A sequence in which the difference of two consecutive terms is constant, is called arithmetic progression.
We use the following notations for an arithmetic progression:
a – the first term
l – the last term
d – common difference
n – the number of terms
Sₙ – the sum of n terms of A.P
Properties of an A.P:
• If a constant is added to each term of an A.P, the resulting sequence is also an A.P.
• If a constant is subtracted from each term of an A.P, the resulting sequence is also an A.P.
• If each term of an A.P is multiplied by a constant, then the resulting sequence is also an A.P.
• If each term of an A.P is divided by a non-zero constant, then the resulting sequence is also an A.P.
• If a, b and c are three consecutive terms of an A.P then
2b = a + c
• Any three terms of an A.P can be taken as (a − d), a, (a + d).
• Any four terms of an A.P can be taken as (a − 3d), (a − d), (a + d), (a + 3d).