Q28 of 176 Page 8

Find a if 5a + 2, 4a – I, a + 2 are in A.P.

Let 5a + 2, 4a – 1, a + 2 are in AP

So, first term a = 5a + 2

d = 4a – 1 – 5a – 2 = – a – 3

n = 3

l = a + 2

So,

l = a + (n – 1)d

⇒ a + 2 =5a + 2 + (3 – 1)(–a – 3)

⇒ a + 2 – 5a – 2 = –3a – 9 + a + 3

⇒ – 4a = –2a – 6

⇒ – 4a + 2a = – 6

⇒ –2a = – 6

⇒ a = 3

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The sum of the 4th and Sth terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of A.P.