The sum of the 2nd and 7th terms of an A.P. is 30. If its 15th term is 1 less than twice its 8th term. Find the A.P.

Question

The sum of the 2 nd and 7 th terms of an A.P. is 30. If its 15 th term is 1 less than twice its 8 th term. Find the A.P.

Philoid · Accepted Answer

The nth term of an A.P. with first term as and common difference as d is given by,

a_n = a + (n – 1) d

⇒ a₂ = a + d

⇒ a₇ = a + 6d

According to question,

⇒ a₂ + a₇ = 30

⇒ a + d + a + 6d = 30

⸫ 2a + 7d = 30 …. (i)

⇒ a₁₅ = a + 14d

⇒ a₈ = a + 7d

According to question,

⇒ a₁₅ = 2a₈ – 1

⇒ a + 14d = 2 (a + 7d) – 1

⇒ a + 14d = 2a + 14d – 1

⸫ a = 1

Substituting the value of a in eq (i), we get

⸫ d = 4

⸫ The terms of the A.P. are 1, 5, 9, 13, 17, 21, …., nth

The sum of the 2^nd and 7^th terms of an A.P. is 30. If its 15^th term is 1 less than twice its 8^th term. Find the A.P.