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if a, b, c are in AP and GP then 

if a, b, c are in AP and GP then  Correct Answer a = b = c

Concept:

1. If a, b, c are in arithmetic progression(AP) then

a + c = 2b

2. If a, b, c are in geometric progression (GP) then

b2 = ac

Calculation:

Given that,

a, b, c are in AP and GP

⇒ a + c = 2b ---(1)

b = √(ac) 

⇒ a + c = 2√(ac)   

Squaring both side

(a + c)2 = 4ac

⇒ a2 + 2ac + c2 = 4ac

⇒ a2 - 2ac - c2 = 0

⇒ (a - c)2 = 0

⇒ a = c

From equation (1)

a = b

Hence, a = b = c.

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