Q. 16 A4.2( 5 Votes )

# If the 8^{th} term of an AP is 31 and its 15^{th} term is 16 more than the 11^{th} term, find the AP.

Answer :

Let the first term and common difference of given AP be a and d respectively.

According to question –

8th term of AP = a_{8} = 31 [Given]

⇒ a + (8 – 1)d = 31

⇒ a + 7d = 31…..(1)

15th term of AP = a_{15} = 16 + a_{11}

⇒ a + (15 – 1)d = 16 + a + (11 – 1)d

⇒ 14d = 16 + 10d

⇒ 4d = 16

∴ d = 4

Substituting the value of d in equation(1), we get –

a = 31 – 7 × 4 = 31 – 28 = 3

Thus, the required AP is 3,7,11,15,…….

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