The 8th term of an A.P. is 37, and its 12th term is 57. Find the A.P.

1.	The 8th term of an A.P. is 37, and its 12th term is 57. Find the A.P.
Answer» We have a₈ = a + (8 – 1)d = a + 7d = 37 …(1) and a₁₂ = a + (12 – 1)d = a + 11d = 57 …(2) Solving the pair of linear equations (1) and (2), we get a + 7d – a – 11d = 37 – 57 ⇒ – 4d = –20 ⇒ d = 5 Putting the value of d in eq (1), we get a + 7(5) = 37 ⇒ a + 35 = 37 ⇒ a = 2 Hence, the required AP is 2, 7, 12, 17,…

Answer»

We have

a₈ = a + (8 – 1)d = a + 7d = 37 …(1)

and a₁₂ = a + (12 – 1)d = a + 11d = 57 …(2)

Solving the pair of linear equations (1) and (2), we get

a + 7d – a – 11d = 37 – 57

⇒ – 4d = –20

⇒ d = 5

Putting the value of d in eq (1), we get

a + 7(5) = 37

⇒ a + 35 = 37

⇒ a = 2

Hence, the required AP is 2, 7, 12, 17,…

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