The sum of first three terms of a G.P. i | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

Answer:

Let the G.P. be a, ar, ar², ar³, …

According to the given condition,

a + ar + ar² = 16 and ar³ + ar⁴ + ar⁵ = 128

⇒ a (1 + r + r2) = 16 … (1)

ar³(1 + r + r2) = 128 … (2)

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

$fraction numerator a r cubed open parentheses 1 plus r plus r squared close parentheses over denominator a open parentheses 1 plus r plus r squared close parentheses end fraction space equals space 128 over 16 rightwards double arrow space r cubed space equals space 8 therefore space r space equals space 2$

Substituting r = 2 in (1), we obtain

a (1 + 2 + 4) = 16

⇒ a (7) = 16

$rightwards double arrow a space equals space 16 over 7 S subscript n space end subscript equals space fraction numerator a open parentheses r to the power of n space minus 1 close parentheses over denominator r minus 1 end fraction rightwards double arrow S subscript n space equals space fraction numerator 16 space over denominator 7 end fraction fraction numerator open parentheses 2 to the power of n space minus 1 close parentheses over denominator 2 minus 1 end fraction space equals space 16 over 7 space open parentheses 2 to the power of n space minus 1 close parentheses$

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Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

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.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Comments

pranav kumar
2017-09-10 10:40:34

In a geometric progression,the sum of first 3 terms is 7 and the sum of next 3 terms is 56.Find the geometric progression.

Jeevan
2017-09-06 19:30:21

This problem help me thank you so much

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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 14: The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine t....

The sum of first three terms of a G.P. i | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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