NCERT Class 11-Math's: Chapter –9 Sequence and Series Part 12

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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)