Question

this question is from arithmetic progression.
1)the sum of three numbers in AP is 30 and ratio of first number to third number is 3:7.find the numbers

Answer 1

(1) Let the 3 numbers in AP be a, a+d and a+2d

Given - 

a + a + d + a + 2d = -3

=> 3a+3d = -3

=> a+d = -1

=> a = -1-d (i)

Also, 

a * (a+d) * (a+2d) = 8

Putting value of (i)

(-1-d) * (-1-d+d) * (-1-d+2d) = 8

=> -(1+d) * -1 * (-1+d) = 8

=> (d+1) * (d-1) = 8

=> d2 - 12 = 8

=> d2 = 9 

∴ d = ±3

If d = +3

a = -1-(+3) [from (i)]= -4

 a+d = -4+3 = -1 and

a+2d = -4+6 = 2

On adding a, a+d and a+2d, we get -4-1+2 = -3. So, d = 3

If d = -3

a = -1-(-3) = 2 [from(i)]

a+d = 2+3 = 5 and

a+2d = 2+6 = 8

On adding a, a+d and a+2d, we get 2+5+8 = 15 ≠ -3. So, d ≠ -3

∴ d = 3 and the AP is -4, -1, 2, ....

Answer 2

let the first number be 3x and
third number be 7x
we know that when three numbers are in ap
then a+c=2b
3x+7x=2b
10x=2b
b=5x
Given sum of three numbers is 30
3x+7x+5x=30
15x=30
x=2

3x=6
5x=10
7x=14

.°.The numbers are 6,10,14