11th Mathematics NCERT Chapter 8
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– Introduction to Sequences: Sequences are ordered collections of objects with identified first, second, third members, etc., and have important applications in various fields【4:0†source】.
– Types of Sequences: Sequences following specific patterns are called progressions. This chapter covers arithmetic progression (A.P.), arithmetic mean, geometric mean, the relationship between A.M. and G.M., and special series involving sums of consecutive natural numbers, squares of natural numbers, and cubes of natural numbers【4:0†source】.
– Finite and Infinite Sequences: Sequences with a finite number of terms are called finite sequences, while those without a finite number of terms are called infinite sequences【4:0†source】.
– Geometric Progression (G.P.): Geometric sequences or geometric progressions (G.P.) are sequences where each term (except the first) bears a constant ratio to the term preceding it. The common ratio is a key aspect of G.P.【4:3†source】.
These topics cover the fundamental concepts of sequences and series discussed in the chapter.
What is the sum of the first 20 terms of the geometric progression 5, 5/2, 5/4, …?
In a Geometric Progression (G.P.) where the 5th, 8th, and 11th terms are denoted as p, q, and s respectively, what relation holds true between q and s?
If the 4th term of a G.P. is the square of its second term and the first term is -3, what is the value of its 7th term?
For what values of x, the numbers (2/7), x, (7/2) form a Geometric Progression (G.P.)?
If the first and nth term of a G.P. are 2 and 128 respectively, what term of the G.P. is 1024?
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