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Question
Find a and b so that the numbers a, 7, b, 23 are in A.P.
Solution
Given, numbers a, 7, b, 23 are in A.P.
∴ 7 – a = b – 7 = 23 – b ...[A.P. has equal common difference]
By equating, b – 7 = 23 – b
⇒ 2b = 30
⇒ b = 15
Now, equating 7 – a = b – 7
⇒ 7 – a = 15 – 7 ...[Putting the value of a]
⇒ – a = 1
⇒ a = –1
Hence, a = –1 and b = 15.
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