Question

Find a and b so that the numbers a, 7, b, 23 are in A.P.

Answer 1

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.