Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2 2 a b a b 4ab 36ab 4ab 32ab a b 32 ab 4 2 ab ...... 2 Adding (1) and (2), we obtain 2 a 6 4 2 a 32 2 ab ab Substituting the value of a b 6 ab 3 2 2 ab b 3 2 2 a b ab 3 2 2 ab 3 2 2 3 2 2 ab 3 2 2 in (1), we obtain Thus, the required ratio is 32 2 : 32 2 . Question 29: If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are Solution 29: A A G A G It is given that A and G are A.M. and G.M. between two positive numbers. Let these two positive numbers be a and b . a b AM A 2 GM G ab ..... 1 .... 2 From (1) and (2), we obtain a b 2 A ..... 3 ab G 2 ....... 4 Substituting the value of a and b 2 2 a b a b 4ab , We obtain a b 2 4A 2 4G 2 4 A 2 G 2 from (3) and (4) in the identity 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 ______________________________________________________________________________ a b 2 4 A G AG a b 2 A G A G ...... 5 From (3) and (5), we obtain 2a 2A 2 A G A G a A A G A G Substituting the value of a in (3), we obtain b 2A A A G A G A A G A G Thus, the two numbers are A A G A G . Question 30: The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2 nd hour, 4 th hour and th n hour? Solution 30: It is given that the number of bacteria doubles every hour. Therefore, the number of bacteria after every hour will form a G.P. Here, a 30 and r 2 2 a ar 2 3 30 2 120 Therefore, the number of bacteria at the end of 2 nd hour will be 120. a 4 ar 4 5 30 2 480 The number of bacteria at the end of 4 th hour will be 480. n a 1 ar 30 2 n n Thus, number of bacteria at the end of th n hour will be 302 n . Question 31: What will Rs. 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually? Solution 31: The amount deposited in the bank is Rs. 500. 1 10 At the end of first year, amount Rs.500 1 Rs.5001.1 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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