Three numbers are in the ratio $2 : 5 : 7$ . If the first number, the resulting number on thesubstraction of $7$ from the second number and the third number form an arithmetic sequence,then find the numbers.

Open in App

Solution

Let the three numbers be $2 x, 5 x$ and $7 x$
It is given that the numbers $2 x, 5 x - 7, 7 x$ are in A.P
Therefore $2 (5 x - 7) = 2 x + 7 x$
$\Rightarrow 10 x - 14 = 9 x$
$\Rightarrow x = 14$
Therefore the numbers are $28, 70, 98$ .

Suggest Corrections

Similar questions

Q. Three numbers whose sum is equal to

28

form a geometric progression. If we add

3

to the first number and

1

to the second and subtract

5

from the third number, the resulting numbers will form an arithmetic progression. Find the numbers.

The second and fourth numbers in an arithmetic sequences are 8 and 2. Find the first and the third numbers.

The second number of and arithmetic sequence is 5. Find the sum of its first and third numbers.

Arithmetic mean of three numbers which are in G.P. is $\frac{14}{3} .$ By adding 1 to the first and second number, and subtracting 1 from the third number, resulting numbers are in A.P. Then sum of squares of original three numbers is

Find the algebraic expression to compute the third number of an arithmetic sequence, using the first and the second numbers.

Join BYJU'S Learning Program

Three numbers are in the ratio 2:5:7. If the first number, the resulting number on thesubstraction of 7 from the second number and the third number form an arithmetic sequence,then find the numbers.

Let the three numbers be 2x,5x and 7xIt is given that the numbers 2x,5x−7,7x are in A.PTherefore 2(5x−7)=2x+7x⇒10x−14=9x⇒x=14Therefore the numbers are 28,70,98.

Three numbers are in the ratio $2 : 5 : 7$ . If the first number, the resulting number on thesubstraction of $7$ from the second number and the third number form an arithmetic sequence,then find the numbers.

Let the three numbers be $2 x, 5 x$ and $7 x$
It is given that the numbers $2 x, 5 x - 7, 7 x$ are in A.P
Therefore $2 (5 x - 7) = 2 x + 7 x$
$\Rightarrow 10 x - 14 = 9 x$
$\Rightarrow x = 14$
Therefore the numbers are $28, 70, 98$ .