According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 8.
Let us assume that there is a generation gap of 25 years, and we are required to find total ancestors that a person might have over 400 years. Here, the total generations = 400/25 = 16. The number of ancestors for the 1st, 2nd, 3rd, . . . 16th generations forms what we call a sequence. The different numbers occurring in a sequence are known as its terms denoted by m1, m2, m3, . . . . . , mn, . . . . . etc. [Here, the position of the term is denoted by the subscript].
A sequence m1, m2, m3, . . . . , mn is said to be an arithmetic sequence or progression if
Also Refer: Sequence and Series
Let us consider an Arithmetic Progression with p as the 1st term and d as the common difference, i.e., p, p + d, p + 2d, . . . . Then the pth term of the A.P. is given by pn = p + (n – 1)d. If a constant term is added, subtracted, multiplied, or divided to an Arithmetic Progression, then the resulting sequence is also an Arithmetic Progression. Given two numbers, p and q. A number A can be inserted between them such that p, A, q is an AP. Such a number is known as the A.M (arithmetic mean) of the numbers p and q. The sum of the 1st n terms of an A.P (Arithmetic Progression) is calculated by
The 1st term of a G.P is denoted by ‘a’ and the common ratio by ‘r’. The general term of a Geometric Progression is given by
The geometric mean of any two +ve numbers p and q are given by G =
To get more details on geometric mean, visit here.
Sequences and Series Class 11 Practice Problems
- If the Geometric and Arithmetic Mean of two +ve numbers p and q are 12 and 10 respectively, find both numbers.
- The fourth term of a Geometric Progression (G.P.) is the square of its 2nd term, and its 1st term is -6. Find its 6th term.
- Determine the sum of n terms of the sequence, 7, 77, 777, 7777, . . . . .
- Determine the sum of n terms of the series: 3 + 9 + 17 + 27 + 39 + . . . .
- Find the 24th term of a sequence defined by pn = (p – 1) (3 + p) (2 – p).
Also, Refer: Sequence and Series Formulas
Related Links:
- Geometric Progression
- Sum of N Terms of AP
- Arithmetic Geometric Sequence
- Difference Between Sequence and Series
- NCERT Exemplar for Class 11 Maths Chapter 9
- NCERT Exemplar for Class 11 Maths Chapter 9
Frequently Asked Questions on CBSE Class 11 Maths Notes Chapter 9 Sequences and Series
What is a Sequence?
It is an arrangement of two or more things in a successive order.
What is a Series?
A series is defined as the sum of the elements of a sequence.
What is a Natural number?
A natural number is a number that occurs commonly and obviously in nature.
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