Which number when added to each of the numbers 7, 14 and 28 would make the sums to be in continued proportion?

Question: Which number when added to each of the numbers 7, 14 and 28 would make the sums to be in continued proportion?

Solution:
Let the number to be added is x.

If three numbers a, b, and c are in continued proportion, then,
a/b = b/c
⇒ b² = ac ..... (1)

Now,
7 + x, 14 + x, 28 + x

From (1) we get,
∴ (14 + x)² = (7 + x)(28 + x)
⇒ 14² + 2 × 14 × x + x² = 7 × 28 + 7x + 28x + x²
⇒ 196 + 35x + x² = 196 + 28x + x²
⇒ 35x = 28x
⇒ 35x - 28x = 0
⇒ 7x = 0
∴ x = 0