Question

If the sum of three consecutive terms of an increasing

a. P is 51 and product of the first and third of these terms is 273, then the third term is

Answer 1

Step-by-step explanation:

Let the three consecutive terms in AP be (a-d), a, (a+d)

According to the given information:

a-d + a + a+d= 51

3a = 51

a = 51/3

a = 17

Since, product of the first and third of these terms is 273.

Therefore,

$- (a - d) \times (a + d) = 273 \\ {a}^{2} - {d}^{2} = 273 \\ {17}^{2} - {d}^{2} = 273 \\ 289 - 273 = {d}^{2} \\ {d}^{2} = 16 \\ d = \pm \: 4 \\ if \: d \: = + 4 \: then \\ \: third \: term \: = a \: + d \: \\ = 17 + 4 = 21 \\ and \: if \: d \: = - 4 \: then \\ \: third \: term \: = a \: + d \: \\ = 17 + ( - 4 ) \\ = 17 - 4 = 13. \\ hence \: the \: third \: term \: of \: ap \: could \: \\ be \: either \: 13 \: or \: 21.$