Web3/1 2 2 2, 5/2 2 3 2, 7/3 2 4 2 , . . . as a difference of two terms. Solution (6) If t k is the kth term of a GP, then show that t n−k, t n, t n+k also form a GP for any positive integer k. Solution (7) If a, b, c are in geometric progression, and if a … Web20 jun. 2024 · Q13. If A is the arithmetic mean and G1 , G2 be two geometric means between any two numbers, then prove that 2A =. Sol: Let the numbers be a and b. Q15. 1f the sum of p terms of an AP. is q and the sum of q terms isp, then show that the sum ofp + q terms is — (p + q). Also, find the sum of first p — q terms (where, p > q).
NCERT Exemplar Class 11 Maths Chapter 9 Sequence and Series
Webpth term, ap = a+(p−1)d qth term, aq =a+(q−1)d rth term, ar =a+(r−1)d Now, according to the question the pth, the qth and the rth terms are in G.P. ∴ (a+(q−1)d)2 =(a+(p−1)d)×(a+(r−1)d) ⇒ a2+2a(q−1)d+((q−1)d)2 = a2+ad(r−1+p−1)+(p−1)(r−1)d2 ⇒ ad(2q−r−p+2)+d2(q2−2q+1−pr+p+r−1)= 0 ⇒ a(2q−r−p)+d(q2−2q−pr+p+r) = 0 ( ∵ d … Web5 jun. 2024 · If Pth, qth and rth terms of an A.P. are in G.P. then the common ratio of this G.P. is ANSWER In AP, first term be a Difference be d ∴pthterm ⇒a+ (p−1)d q th term a+ (q−1)d r thterm a+ (r−1)d Since they are in GP and let first term in G.P be A and common ration be r ∴ As given a+ (p−1)d=A... (1) a+ (q−1)d=Ar... (2) a+ (r−1d)=Ar ²... (3) my northside 360
If the pth, qth and rth term of a GP are a, b, c respectively
WebQ. If pth,qth rth terms of an A.P. are equal to corresponding terms of a G.P. and these terms are respectively x, y, z, then xy−z ⋅ yz−x ⋅ zx−y equals 1656 50 Sequences and Series Report Error A 0 B 1 C 2 D None of these Solution: Let first term of an A.P. be a and c.d. be d and first term of a G.P. be A and c.r. be R,then a +(p− 1)d = ARp−1 = x Web30 mrt. 2024 · 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 … WebIf the p th and q th terms of a G.P. are q and p, respectively, then show that (p + q)th term is ( q p p q) 1 p − q. VIEW SOLUTION Exercise 20.2 [Page 16] RD Sharma solutions for Class 11 Mathematics Textbook Chapter 20 Geometric Progression Exercise 20.2 [Page 16] Exercise 20.2 Q 1 Page 16 old record player cartoon