Question

four terms are in ap. if sum of numbers is 50 and largest number is four times the smaller one, then find the terms

Answer 1

Answer:

terms are 5,10,15,20

Step-by-step explanation:

let the 4 no's be a-3d , a-d , a+d , a+3d

then a-3d+a-d+a+d+a+3d=50 

4a=50

a=25/2

but a+3d=4(a-3d)

a+3d=4a-12d

3a=15d

a=5d

25/2=5d

d=5/2 

so the 4 no's are

a-3d=25/2-15/2=10/2=5

a-d=25/2-5/2=20/2=10

a+d= 25/2+5/2=15

a+3d= 25/2+15/2=20

Answer 2

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

Solution:

In arithmetic progression, difference between terms is constant

Let the 4 numbers are a , a + d , a + 2d , a + 3d

Sum of 4 numbers AP = 50

a + a + d + a + 2d + a + 3d = 50

4a + 6d = 50

2a + 3d = 25 ------ eqn 1

Also given the largest number is 4 times the smaller one

largest one = a + 3d

smaller one = a

4(a) = a + 3d

4a - a = 3d

a = d

Substitute a = d in eqn 1

2d + 3d = 25

5d = 25

d = 5

Since, a = d

a = 5

Thus the numbers are:

a = 5

a + d = 5 + 5 = 10

a + 2d = 5 + 2(5) = 5 + 10 = 15

a + 3d = 5 + 3(5) = 5 + 15 = 20

Thus first four terms are 5 , 10 ,15 , 20

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