arithmetic progression

Let us learn about arithmetic progression

An Arithmetic progression which consists of the sequence & the terms except the 1st can be obtained by adding 1 numbe! r to its preceding number. Arithmetic progression is denoted as the arrangement of 2 consecutive numbers, the progression which is constant. Sequence of numbers such that the difference of any 2 successive members of the sequence is a constant

If a, b, c are in A.P then prove that (a–c)² = 4(b² – ac)

Solution: a, b, c are in A.P

⇒ b – a = c – b = common difference

⇒ 2b = a + c

⇒ 4b² = a² + 2ac + c^{2 (}Squaring both sides)

⇒ 4b² – 4ac = a² – 2ac + c² ( Subtracting 4ac on both sides)

⇒ 4(b² – ac) = (a – c)² ( Taking 4 common)

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