The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.
The sum of the first three terms of the G.P. is 39 10 and their product is 1 .
Let the first term and common ratio of the given G.P. be a and r respectively.
Let the three consecutive terms of the G.P. be a r , a , a r .
As per the question,
a r + a + a r = 39 10 ( a r ) ( a ) ( a r ) = 1 a 3 = 1
Solve the above equations to obtain a and r .
a = 1 1 r + r + 1 = 39 10 1 + r + r 2 = 39 10 r 10 + 10 r + 10 r 2 = 39 r
Further simplify the above expression.
10 r 2 − 29 r + 10 = 0 10 r 2 − 25 r − 4 r + 10 = 0 5 r ( 2 r − 5 ) − 2 ( 2 r − 5 ) = 0 ( 5 r − 2 ) ( 2 r − 5 ) = 0
Equate the terms on both the sides.
r = 2 5 or 5 2
The terms are obtained by using the values of a and r .
5 2 , 1 , 2 5
Thus, the three terms of the G.P. are 5 2 , 1 , 2 5 .
The sum of the first three terms of the G.P. is
Let the first term and common ratio of the given G.P. be
Let the three consecutive terms of the G.P. be
As per the question,
Solve the above equations to obtain
Further simplify the above expression.
Equate the terms on both the sides.
The terms are obtained by using the values of
Thus, the three terms of the G.P. are
