NCERT Class 11-Math՚S: Chapter – 9 Sequence and Series Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 16:

If , and terms of an A. P. and G. P. are both and respectively, show that

Answer:

Let the first term of AP be m and common difference as d

Let the GP first term as l and common ratio as s

The nth term of an AP is given as where a is the first term and d is the common difference

The nth term of a GP is given by where a is the first term and is the common ratio

The term of both AP and GP is a

For AP

For GP

The term of both AP and GP is b

For AP

For GP

The term of both AP and GP is c

For AP

For GP

Let us find and

Using (w) and (y)

Using (y) and (u)

Using (u) and (w)

We have to prove that

LHS

Using (v) , (x) and (z)

Substituting values of a – b, c – a and b – c from (iii) , (ii) and (i)

Hence proved

Objective Type Questions

Choose the Correct Answer Out of the Four Given Options in Each of the Exercises 17 to 26 (M. C. Q.)

Question 17:

If the sum of n terms of an A. P. is given by

, then the common difference of the A. P. is

(A)

(B)

(C)

(D)

Answer: (D)