Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2 a 1 r A2 4 ...... 1 1 r a 4a 5 3 4 2 2 ar ar r r 2 4 4 From (1), we obtain 2 a 1 2 4 1 2 a 4 1 4 1 4 a 3 a Also, 4 3 for a 1 2 4 1 2 a 1 4 4 1 2 a 3 4 3 a 4 r 2 2 Thus, the required G.P. is for r 2 4 8 16 , , ,... 3 3 3 or 4, 8, 16, 32... Question 17: If the 4 th , 10 th and 16 th terms of a G.P. are xy, , and z, respectively. Prove that Solution 17: Let a be the first term and r be the common ratio of the G.P. According to the given condition, a a r x 3 4 ...... 1 a a r y 9 10 ...... 2 a a r z 15 16 ...... 3 Dividing (2) by (1), we obtain x, y, z are in G.P. 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 ______________________________________________________________________________ y 9 ar y x 3 ar x r Dividing (3) by (2), we obtain z 15 ar z y 9 ar y r y z x y Thus, x, y, z are in G.P. 6 6 Question 18: Find the sum to n terms of the sequence, 8, 88, 888, 8888 …. Solution 18: The given sequence is 8, 88, 888, 8888 …. This sequence is not a G.P. However, it can be changed to G.P. by writing the terms as S 888 888 8888 ...... n to n terms 8 9 99 999 9999 .......to n terms 9 2 3 4 8 10 1 10 1 10 1 10 1 .......to n terms 9 8 10 10 2 ....... n terms 1 1 1 ..... n terms 9 n 8 10 10 1 9 10 1 n 8 10 10 1 9 9 n n 80 10 1 8 n n 81 9 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 12 - Introduction

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