Find the value of P for which the numbers 2P-1 ,3P+1, 11, are in AP. Hence find the number
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FORMULA :If the numbers a, b and c are in AP, thenb – a = c – b=> 2b = a + cSOLUTION :The given three numbers (2p – 1), (3p + 1) and 11 are in AP.Then,2(3p + 1) = (2p – 1) + 11=> 6p + 2 = 2p – 1 + 11=> 6p + 2 = 2p + 10=> 6p – 2p = 10 – 2=> 4p = 8=> p = 8/4=> p = 2So, the value of p is 2.Then, the given numbers be(2×2 – 1), (3×2 + 1) and 11i.e., 3, 7 and 11.So, we get an Arithmetic progression 3, 7, 11.
P=2 3,7,11??