Question

please solve this one ​

Answer 1

QUESTION:

If a, b, c are in A.P and also 1/a, 1/b, 1/c are in A.P, then

GIVEN:

• a, b, c are in A.P.

• 1/a, 1/b, 1/c are in A.P.

FORMULA:

$Common\:\:difference\:\:d = t_2 - t_1=t_3 - t_2$

EXPLANATION:

• a, b, c are in A.P

• d = b - a = c - b

• 2b = a + c

• b = (a + c)/2

• 1/a, 1/b, 1/c are in A.P

• d = 1/b - 1/a = 1/c - 1/b

• 1/b + 1/b = 1/a + 1/c

• 2/b = (a + c)/ac

• 2ac = b(a + c)

• Substitute b = (a + c)/2

• 2ac = (a + c)(a + c)/2

• 4ac = (a + c)²

• 4ac = a² + 2ac + c²

• a² - 2ac + c² = 0

• (a - c)² = 0

• a - c = 0

• a = c

• Substitute a = c in 2b = a + c

• 2b = 2a

• b = a

HENCE a = b = c