Question

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are
(a) 5, 10, 15, 20
(b) 4, 101, 16, 22
(c) 3, 7, 11, 15
(d) none of these

Answer 1

Answer:

The first four terms are 5, 10, 15, 20.

Among the given options option (a) 5, 10, 15, 20 is correct.  

Step-by-step explanation:

Let the 4 numbers in A.P are a, (a + d) , (a + 2d), (a + 3d).

Given :  

Sum of 4 numbers in A.P = 50

a + (a + d) + (a + 2d )+ (a + 3d) = 50

⇒ 4a + 6d = 50

⇒2(2a + 3d) = 50

⇒(2a + 3d) = 50/2

⇒ 2a + 3d = 25 …………...(1)

Given : Greatest number is 4 times the least.

a + 3d = 4a

4a – a = 3d

3a = 3d

a = 3d/3

a = d

On putting, a = d in eq 1,  

2a + 3d = 25

2d + 3d = 25

5d = 25

d = 25/5

d = 5

⇒a = d =  5

1st term  = a = 5  

2nd term = a + d = 5 + 5 = 10

3rd term = a + 2d = 5 + 2×5 = 5 + 10 = 15

4th term = a + 4d = 5 + 4 × 5 = 5 + 20 = 25

Hence, the first four terms are 5, 10, 15, 20.

HOPE THIS ANSWER WILL HELP YOU….

 

Answer 2

Answer :

The sum of 4 number in A .P = 50

a+(a+b) + ( a+2d ) + (a + 3d) =50

=4a + 6d = 50

2(2a + 3d ) = 50

( 2a + 3d ) = 50 / 2

2a + 3d = 25

Greatest number is 4 times the least

a+ 3d = 4a

4a - a = 3d

3a = 3d

a = 3d / 3

a= d

Before putting a = d in equal 1

2a + 3d = 25

2d + 3d = 25

5d = 25

D = 25 / 5

D= 25 = 5

5

D= 5

1st term = a=5

2nd term = a+d=5+5 = 10

3rd term = 5+2×5 = 5+10= 15

4th term = a+4d = 5+4 × 5 = 5 = 25

So ,

Answer is (A)

because answer is = 5,10,15,20.