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Arithmetic Progressions

Question
CBSEENMA10007967

For what value of k, are the numbers x, 2x + k and 3x + 6 three consecutive terms of an A .P

Solution

x, 2x + k,3x + 6 are in A .P. if
(2x + k) – x = (3x + 6) – (2x + k)
⇒ 2x + k – x = 3x + 6 – 2x – k
⇒ x + k = x + 6 – k
⇒ 2k = 6
⇒ k = 3