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nth Term of an AP

If 2 p+1, 13,...

Question

If $(2 p + 1), 13, (5 p - 3)$ are three consecutive terms of an AP, then p = ?
(a) 4
(b) 5
(c) 6
(d) 3

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Solution

(a) 4
If (2p + 1), 13 and(5p - 3) are three consecutive terms of an AP, then we have:
13 - (2p+1) = (5p-3) - 13
⇒ 12 - 2p = 5p - 16
⇒ 7p = 28
⇒ p = 4

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