Question

Find an AP whose sum of first 3 terms is 21 and sum of their squares is 155.

Answer 1

Q). If the sum of three numbers of an ap is 21 and sum of their squares is 155 find the numbers

Answer 2

Given:

Sum of first three terms = 21

Sum of its squares = 155

To Find:

AP

Solution:

Let the three terms of AP be = a-d, a , and a+d

According to question,

a - d + a + a + d = 21

3a = 21

a = 7

Thus,

(a - d)² +a² + (a +d)² = 155

3a² -2d² = 155

Substituting the value -

3 (7)² -2d² = 155

147 -2d² = 155

2d² = 155 - 147

2d² = 8

d² = 4

d = 2

Therefore, the numbers are -

7-2 , 7 , 7+2

Answer: The AP is 5 , 7 , 9