A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
The sum of first three terms of a G.P is 39/10 and their product is 1. Find the common ratio and the terms
Solution:
Let a/r, a, ar be the first three terms of the G.P.
It is given that a/r + a + ar = 39/10 ....(1)
(a/r) (a) (ar) = 1 ....(2)
From (2), we obtain
a3 = 1
⇒ a = 1 (considering real roots)
Substituting a = 1 in (1), we obtain
⇒ 1/r + 1 + r = 39/10
⇒ 1 + r + r2 = 39/10 r
⇒ 10 + 10r + 10r2 - 39r = 0
⇒ 10r2 - 29r + 10 = 0
⇒ 10r2 - 25r - 4r + 10 = 0
⇒ 5r (2r - 5) - 2 (2r - 5) = 0
⇒ (5r - 2)(2r - 5) = 0
r = 2/5, 5/2
Thus, the three terms of the G.P are 2/5, 5/2
NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 12
The sum of first three terms of a G.P is 39/10 and their product is 1. Find the common ratio and the terms
Summary:
It is given that the sum of first three terms of a G.P is 39/10 and their product is 1. Thus, the common ratio is 2/5, 5/2
Math worksheets and
visual curriculum
visual curriculum