LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
64 views
in Sequences and series by (17 points)
The sum of first four terms of a geometric progression (G.P.) is \( \frac{65}{12} \) and the sum of their respective reciprocals is \( \frac{65}{18} \). If the product of first three terms of the G.P. is 1 , and the third term is \( \alpha \), then \( 2 \alpha \) is [JEE Mains (Feb) 2021]

Please log in or register to answer this question.

1 Answer

0 votes
by (45.5k points)

Let the terms of the GP be α, αr, αr2, αr3

Therefore from the given condition we have

The sum of the first four terms is

The sum of the reciprocal of the first four term is

Dividing (i) by (ii) we get,

Given that the product of the first three terms is 1

Using result (iii) & (iv) we get

α = 2/3

Putting the value of α in (iv) we get,

r = 3/2

From given

Hence, the value of 2α is 3.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...