Question 1: The sum of three terms of an A.P. is and the product of the first and the third terms exceeds the second term by , find three terms.

Answer:

Let the three terms of the A.P. be

Also

When , the three terms are

When , the three terms are

Question 2: Three numbers are in A.P. If the sum of these numbers be and the product , find the numbers.

Answer:

Let the three terms of the A.P. be

Also

When , the three terms are

When , the three terms are

Question 3: Find the four numbers in A.P., whose sum is and in which the greatest number is times the least.

Answer:

Let the four numbers be

Also

the terms are or

Question 4: The sum of three numbers in A.P. is and the sum of their cubes is . Find the numbers.

Answer:

Let the three terms of the A.P. be

Also

When , the three terms are

When , the three terms are

Question 5: If the sum of three numbers in A.P. is and their product , find the numbers.

Answer:

Let the three terms of the A.P. be

Also,

When , the three terms are

When , the three terms are

Question 6: The angles of a quadrilateral are in A.P. whose common difference is . Find the angles.

Answer:

Let the angles be

Given

Sum of the angles

Therefore the angles are .