Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+2 votes
13.8k views
in Mathematics by (69.4k points)

The sum of the 3rd and the 4th terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its 7th term is :

(1)  7290

(2)  640

(3)  2430

(4)  320

2 Answers

+1 vote
by (64.1k points)
selected by
 
Best answer

Correct option  (4) 320

Explanation:

+1 vote
by (1.3k points)
We have,

a.r^2 + a.r^3 = 60

a.r^2 (1 + r) = 60                         ......(1)

Also,

a × ar × a.r^2 = 1000

(ar)^3 = (10)^3

ar = 10

a = 10/r                                       ......(2)

Substituting this value of a in equation (1), we get

10/r × r^2 (1 + r) = 60

r(r + 1) = 6

r^2 + r - 6 = 0

r^2 + 3r - 2r - 6 = 0

r(r + 3) - 2(r + 3) = 0

(r - 2)(r + 3) = 0

r = 2, -3

Putting both the values of r in equation (1), we get

a = 10/2            and          a = -10/3

a = 5, -10/3

We will take a = 5 because a is positive (according to the question).

Now,

7th term = a.r^6 = 5 × 2^6 = 5 × 64 = 320

So, the correct option is (4) 320.

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.

Categories

...