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Find a G.P. for which sum of the first two terms is –4 and the f...

Find a G.P. for which sum of the first t | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.

Answer:

Let a be the first term and r be the common ratio of the G.P.

According to the given conditions,

$S subscript 2 space equals space minus 4 space equals space fraction numerator a open parentheses 1 minus r squared close parentheses over denominator 1 minus r end fraction space space space space space space space space space... left parenthesis 1 right parenthesis a subscript 5 space equals space 4 space cross times space a subscript 3 a r to the power of 4 space equals space 4 a r squared rightwards double arrow r squared space equals space 4 therefore space r space equals space plus-or-minus 2$

From (1), we obtain

$minus 4 space equals space fraction numerator a open square brackets 1 minus open parentheses 2 close parentheses squared close square brackets over denominator 1 minus 2 end fraction space f o r space r space equals 2 rightwards double arrow minus 4 space equals space fraction numerator a open parentheses 1 minus 4 close parentheses over denominator minus 1 end fraction rightwards double arrow minus 4 space equals space a open parentheses 3 close parentheses rightwards double arrow a space equals space fraction numerator minus 4 over denominator 3 end fraction A l s o comma space minus 4 space equals space fraction numerator a open square brackets 1 minus open parentheses minus 2 close parentheses squared close square brackets over denominator 1 minus open parentheses minus 2 close parentheses end fraction space f o r space r space equals minus 2 rightwards double arrow minus 4 space equals space fraction numerator a open parentheses 1 minus 4 close parentheses over denominator 1 plus 2 end fraction rightwards double arrow minus 4 space equals space fraction numerator a open parentheses minus 3 close parentheses over denominator 3 end fraction rightwards double arrow a space equals space 4 T h u s comma space t h e space r e q u i r e d space G. P. space i s fraction numerator minus 4 over denominator 3 end fraction comma space fraction numerator minus 8 over denominator 3 end fraction comma space fraction numerator minus 16 over denominator 3 end fraction space comma space... space o r space 4 comma space minus 8 comma space 16 comma space minus 32 comma space...$ .....

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Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Sequence and Series.
Review previous year question papers to get an idea of how such questions may be framed in exams.
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Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Comments

Reply for yoyo
2017-10-28 21:08:57

Peace bro

yo yo
2016-10-14 02:13:15

cool brooo

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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 3 , Question 16: Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third....

Find a G.P. for which sum of the first t | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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