The 5th, 8th and 11th terms of | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q² = ps.

Answer:

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

According to the given condition,

a₅ = a r⁵–1 = a r⁴ = p … (1)

a₈ = a r⁸–1 = a r⁷ = q … (2)

a₁₁ = a r¹¹–1 = a r¹⁰ = s … (3)

Dividing equation (2) by (1), we obtain

$fraction numerator a r to the power of 7 over denominator a r to the power of 4 end fraction equals q over p r cubed equals q over p space space space space space space... left parenthesis 4 right parenthesis$

Dividing equation (3) by (2), we obtain

$fraction numerator a r to the power of 10 over denominator a r to the power of 7 end fraction equals s over q rightwards double arrow r cubed equals s over q space space space space space space space... left parenthesis 5 right parenthesis$

Equating the values of r3 obtained in (4) and (5), we obtain

$q over p equals s over q rightwards double arrow q squared equals p s$

Thus, the given result is proved.

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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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Comments

Sandhya
2019-03-07 16:37:33

Thank you for answer

Suyash singh
2018-10-24 19:47:00

Excellent

Raunak singh
2018-09-13 21:54:39

Super

Akanksha singh tomar
2018-08-30 11:40:15

Very nice

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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 3: The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Sh....

The 5th, 8th and 11th terms of | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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