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NCERT Solutions for Class 11 Math Ch-8: Sequences and Series
NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series covers arithmetic progressions (AP), geometric progressions (GP), their nth terms and sums, and the relationship between arithmetic and geometric means.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: What is the formula for the nth term of an Arithmetic Progression (AP)?
Answer: The nth term of an AP with first term 'a' and common difference 'd' is given by an = a + (n − 1)d.
Q2: What is the formula for the sum of the first n terms of an AP?
Answer: The sum of the first n terms of an AP is given by Sn = (n/2)[2a + (n − 1)d], or equivalently Sn = (n/2)(a + l), where 'l' is the last term of the series.
Q3: What is the formula for the nth term of a Geometric Progression (GP)?
Answer: The nth term of a GP with first term 'a' and common ratio 'r' is given by an = a·r^(n−1).
Q4: What is the formula for the sum to infinity of a GP, and under what condition is it valid?
Answer: The sum to infinity of a GP is given by S∞ = a / (1 − r), and this formula is valid only when the absolute value of the common ratio is less than 1, i.e., |r| < 1, ensuring the series converges to a finite value.
Q5: What is the relationship between the Arithmetic Mean (AM) and Geometric Mean (GM) of two positive numbers?
Answer: For any two positive real numbers, the Arithmetic Mean is always greater than or equal to the Geometric Mean (AM ≥ GM), with equality holding only when the two numbers are equal.
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