Three numbers in

We know that the sum of 3 numbers in the AP is 18.

Let’s say that those 3 numbers are: a – d, a, a + d

So we can say that, a – d + a + a + d = 18

3a = 18

a= 6

Now, we have that the sum of squares of these 3 numbers is 180.

So we can say that, (a – d) 2 + a2 + (a + d) 2 = 180

a2 – 2ad + d2 + a2 + a2 + 2ad + d2 = 180

3a2 + 2d2 = 180

We know that a = 6,

So, 3(6)2 + 2d2 = 180

3(36) + 2d2 = 180

108 + 2d2 = 180

2d2 = 180 – 108

2d2 = 72

d2 = 36

d = 6

Now, our 3 numbers a – d, a, a + d are 6 – 6, 6, 6 + 6 = 0, 6, 12 respectively.

The 3 numbers of the A.P in the increasing order are : 0, 6, 12.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Arithmetic Progression- Don't miss these Questions56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

In an A.P. 5th teGujarat Board Mathematics

Which term of A.PGujarat Board Mathematics

If in an A.P., T<Gujarat Board Mathematics

If in an A.P., T<Gujarat Board Mathematics

Find the 10th terGujarat Board Mathematics

Which term of A.PGujarat Board Mathematics

Can any term of AGujarat Board Mathematics

If for A.P., T<suGujarat Board Mathematics

For A.P. T18Gujarat Board Mathematics

Find the nth termGujarat Board Mathematics