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The 17th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, then what is its nth term?

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− 4 n − 1

4 n − 1

4 n + 1

− 4 n + 1

answer is D.

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Detailed Solution

Given that the 17th term of AP is 5 more than twice its 8th term and 11th term of A.P. is 43.
Let first term be a and common difference be d.
As from first given condition:

∴ a 17 = 2 a 8 + 5

Formula used for

n t h

term of A.P.:

a n = a + n − 1 d

Applying the formula of nth term of AP and calculate:

∴ a + (17 − 1) d = 2 {a + (8 − 1) d} + 5 ⇒ a + 16 d = 2 a + 14 d + 5 ⇒ a = 2 d − 5 − − − − (1)

Now, from second given condition:

∴ a 11 = 43

Applying the formula of nth term of AP and calculate:

∴ a + (11 − 1) d = 43 ⇒ a + 10 d = 43 − − − − (2)

Putting the value from equation (1) in equation (2):

∴ 2 d − 5 + 10 d = 43 ⇒ 12 d = 48 ⇒ d = 4

Putting the value of d in equation (1):

∴ a = 2 × 4 − 5 ⇒ a = 8 − 5 = 3

Formula used for

n t h term of A .P:

∴ a n = 3 + (n − 1) × 4 ⇒ a n = 3 + 4 n − 4 = 4 n − 1

Therefore, the

n t h term of A .P

is 4n – 1.
Hence, option (4) is correct.

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