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)