If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is

Let 3 consecutive terms A.P is a –d, a, a + d. and the sum is 51


So, (a –d) + a + (a + d) = 51


3a –d + d = 51


3a = 51


a = 17


The product of first and third terms = 273


So, (a –d) (a + d) = 273


a2 –d2 = 273


172 –d2 = 273


289 –d 2 = 273


d2 = 289 –273


d2 = 16


d = 4


Third term = a + d = 17 + 4 = 21

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