# Misc 9 - Chapter 9 Class 11 Sequences and Series (Term 1)

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 9 The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P. It is given that Sum of third term & fifth term is 90 i.e. a3 + a5 = 90 We know that nth term of GP = arn – 1 i.e. an = arn – 1 Putting n = 3 & a = 1 a3 = 1 r3 – 1 = r2 Putting n = 5 & a = 1 a5 = 1.r5 – 1 a5 = r4 Putting a3 & a5 in (1) a3 + a5 = 90 r2 + r4 = 90 r4 + r2 – 90 = 0 Let r2 = x So, our equation becomes x2 + x – 90 = 0 x2 + 10x – 9x – 90 = 0 x(x + 10) – 9(x + 10) = 0 (x – 9)(x + 10) = 0 (x – 9)(x + 10) = 0 Hence the common ratio is -3 and 3

Miscellaneous

Misc 1

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Misc 3 Important

Misc 4

Misc 5

Misc 6 Important

Misc 7 Important

Misc 8

Misc 9 You are here

Misc 10 Important

Misc 11

Misc 12

Misc 13

Misc 14 Important

Misc 15

Misc 16 Important

Misc 17

Misc 18

Misc 19 Important

Misc 20

Misc 21 (i) Important

Misc 21 (ii)

Misc 22 Important

Misc 23 Important

Misc 24 Deleted for CBSE Board 2022 Exams

Misc 25 Important Deleted for CBSE Board 2022 Exams

Misc 26 Deleted for CBSE Board 2022 Exams

Misc 27

Misc 28 Important

Misc 29 Important

Misc 30

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Misc 32 Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.