Chapter 9 Class 11 Sequences and Series
Question 5 Important Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 15 Important Deleted for CBSE Board 2024 Exams
Question 17 Deleted for CBSE Board 2024 Exams
Example 9 Important
Example 10 Important
Ex 8.2, 3 Important
Ex 8.2, 11 Important
Ex 8.2, 17 Important
Ex 8.2, 18 Important
Ex 8.2, 22 Important You are here
Ex 8.2, 28
Ex 8.2, 29 Important
Ex 9.4.4 Important Deleted for CBSE Board 2024 Exams
Question 7 Important Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 10 Deleted for CBSE Board 2024 Exams
Question 9 Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Misc 10 Important
Question 13 Important Deleted for CBSE Board 2024 Exams
Misc 14 Important
Misc 18 Important
Chapter 9 Class 11 Sequences and Series
Last updated at April 16, 2024 by Teachoo
Ex9.3, 22 If the pth ,qth and rth terms of a G.P. are a, b and c, respectively. Prove that aq r br p cp q = 1 We know that nth term of G.P = ARn 1 (We are using a, r in the question, so we use A for first term and R for common ratio) It is given that pth term of G.P = a Ap = a ARp 1 = a a = ARp 1 aq r = ("ARp 1")q r We need to show that aq r br p cp q = 1 Also, qth term of G.P = b Aq = b ARq 1 = b b = ARq 1 br p = (ARq 1)r p & rth term of G.P = c Ar = c ARr 1 = c c = ARr 1 cp q = (ARr 1)p q Now, our equations are aq r = ("ARp 1")q r (1) br p = (ARq 1)r p (2) & cp q = (ARr 1)p q (3) Taking L.H.S. aq r br p cp q Putting values from (1), (2) & (3) = ("ARp 1")q r (ARq 1)r p (ARr 1)p q = "Aq r R(p 1")(q r) "Ar p R(q 1")(r p) "Ap q R(r 1")(p q) = "Aq r Ar p Ap q " "R(p 1")(q r) "R(q 1")(r p) "R(r 1")(p q) = A(q r) + (r p) + (p q) R(p 1) (q - r) + (q 1) ( r - p) + (r 1) ( p-q) = A(q r) + (r p) + (p q) Rp(q r ) 1(q r) + q( r p) 1(r p) +r(p q) 1( p q) = A(q q) + (r r) + (p p) Rpq pr q + r + qr qp r + p + rp qr p + q = A0 R pq pq q + q + r r + p p + qr qr + qp qr = A0 R0 = 1 1 = 1 = R.H.S Thus, L.H.S = R.H.S Hence proved