Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ Question 19: Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2. Solution 19: Required sum 1 1 64 4 2 1 2 2 2 Here, First term, 1 1 4, 2,1, , 2 2 2 a 4 Common ratio, It is known that, 1 2128 432 88 16 2 32 2 1 r 2 S n is a G.P. a 1 r 1 r 5 1 41 1 2 41 32 32 1 31 S5 8 1 1 1 32 4 2 2 n 31 64 16 31 496 4 Required sum Question 20: Show that the products of the corresponding terms of the sequences form A, AR, AR , AR 2 n 1 Solution 20: a G.P, and find the common ratio. It has to be proved that the sequence: Second term First term Third term Second term ar AR rR aA 2 2 ar AR rR arAR a, ar, ar ,..... ar 2 n 1 2 2 n1 n 1 aA, arAR, ar AR , ....... ar AR , forms a G.P. Thus, the above sequence forms a G.P. and the common ratio is rR. and Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ Question 21: Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4 th by 18. Solution 21: Let a be the first term and r be the common ratio of the G.P. a a, a ar, a ar , a ar 2 3 1 2 3 4 By the given condition, a a ar a 2 3 1 9 9 ..... 1 a a ar ar 3 4 4 18 18 ..... 2 From (1) and (2), we obtain 2 1 9....... 3 a r ar 2 1r 18....... 4 Dividing (4) by (3), we obtain ar a r 2 1 r 18 2 1 r 2 r 2 9 Substituting the value of r in (1), we obtain 4aa 9 3a 9 a 3 Thus, the first four numbers of the G.P. are i.e., 3, 6,12 and 24. 2 3, 3 2 , 3 2 , and 32 3 Question 22: If th p , th q and th r terms of a G.P. are ab , Solution 22: Let A be the first term and R be the common ratio of the G.P. According to the given information, p AR q AR r AR 1 a 1 1 b c qr r p pq and c , respectively. Prove that a b c 1. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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