The sum of three numbers in gp is 56

Asked by admin @ 11/08/2021 in Math viewed by 303 People

Question 10 The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

Class X1 - Maths -Sequences and Series Page 199

Answered by admin @ 11/08/2021

Let three numbers in GP are a , ar , ar².
Given, a + ar + ar² = 56
a(1 + r + r²) = 56 --------------------(1)

A/C to question,
(a - 1) , (ar - 7), ( ar² - 21) are in AP
so, common difference is always constant.
e.g (ar² - 21) - (ar - 7) = (ar - 7) - (a - 1)
ar² - ar - 21 + 7 = ar - a - 7 + 1
ar² - 2ar + a - 8 = 0
a( r² - 2r + 1) = 8 --------------------(2)

dividing equation (1) by equation (2) , we get
a( 1 + r + r²)/a(r² - 2r + 1) = 56/8
(1 + r + r²)/(1 - 2r + r²) = 7
1 + r + r² = 7 - 14r + 7r²
6r² - 15r + 6 = 0
2r² - 5r + 2 = 0
2r² - 4r - r + 2 = 0
2r( r - 2) -(r - 2) = 0
(2r - 1)(r - 2) = 0
r = 2, 1/2

if r = 2 then, from equation (1)
a + 2a + 4a = 56
7a = 56
a = 8

Then, numbers are a = 8
ar = 8 × 2 = 16
ar² = 8 × 2² = 32
hence, 8 , 16 , 32

similarly if r = 1/2 then from equation (1)
a + a/2 + a/4 = 56
7a/4 = 56
a = 32

then, numbers are 32 , 32 × 1/2 , 32 × 1/2²
32 , 16 , 8

The sum of three numbers in gp is 56

Similar Questions

Three numbers are in gp whose sum is 70

The sum of 3 numbers in gp is 56

Three numbers whose sum is 21 are in ap

The sum of four numbers in gp is 60

Find three consecutive even numbers whose sum is 96

The sum of three numbers in ap is 3

The sum of three consecutive even numbers is 48

Find three consecutive even numbers whose sum is 234

The sum of three numbers in ap is 12

The sum of three odd number is even

The product of three numbers in gp is 216

Find three consecutive odd number whose sum is 147

Find three consecutive odd numbers whose sum is 147

The sum of two consecutive odd numbers is 56

Which three-dimensional figure has double the number of edges as faces?

Most viewed questions in Math

What is the value of x in the expression

Shubham is facing south and moves 30 km

Prachi excellence in mathematics class 7 solutions pdf free download

Oxford new enjoying mathematics class 7 solutions chapter 1

Survey of various types of bank accounts icse project

The town of p is located at point x

A clock gains 4 minutes after every 4 minutes

Running a tuck shop or canteen maths project pdf

Paul is sixteenth from the front of the row

The average weight of 20 teachers is 80 kg

The number 567 xy is completely divisible by 30

In a row of friends tiya occupies fifteenth place

What would $ mean if fat is coded as

Consider a 3 digit integer x with distinct digits

Rahul went to his mother's mother in law