The 7th term of an A.P. is 20 and its 13th term is 32. Find the A.P.

1.	The 7th term of an A.P. is 20 and its 13th term is 32. Find the A.P.
Answer» We have a₇ = a + (7 – 1)d = a + 6d = 20 …(1) and a₁₃ = a + (13 – 1)d = a + 12d = 32 …(2) Solving the pair of linear equations (1) and (2), we get a + 6d – a – 12d = 20 – 32 ⇒ – 6d = –12 ⇒ d = 2 Putting the value of d in eq (1), we get a + 6(2) = 20 ⇒ a + 12 = 20 ⇒ a = 8 Hence, the required AP is 8, 10, 12, 14,…

Answer»

We have

a₇ = a + (7 – 1)d = a + 6d = 20 …(1)

and a₁₃ = a + (13 – 1)d = a + 12d = 32 …(2)

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

a + 6d – a – 12d = 20 – 32

⇒ – 6d = –12

⇒ d = 2

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

a + 6(2) = 20

⇒ a + 12 = 20

⇒ a = 8

Hence, the required AP is 8, 10, 12, 14,…

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