Find the value of P for which the numbers 2P-1 ,3P+1, 11, are in AP. Hence find the number

Find the value of P for which the numbers 2P-1 ,3P+1, 11, are in AP. H

1.	Find the value of P for which the numbers 2P-1 ,3P+1, 11, are in AP. Hence find the number
Answer» 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??