Question

the sum of three consective term in AP is 6 and their product is -120 find the three numbers ​

Answer 1

Answer:

Let the three consecutive number of ab be,

a-d , a, a +d

Thus,

$a - d + a + a + d = 6 \\ \\ 3a = 6 \\ \\ a = 2$

Thus, first term (a) is 2.

By given info,

$(a - d) \times (a + d) \times a = - 120 \\ \\ a {}^{2} - d {}^{2} \times a = - 120 \\ \\ a {}^{3} - d {}^{2} a = - 120 \\ \\ 2 {}^{3} - 2 \times d {}^{2} = - 120 \\ \\ d {}^{2} = \frac{ 128}{2 } \\ \\ d = 8 \: \: and \: - 8$

If, we take d = 8, The info given does not match.

Thus, d = -8

So, The A.P is 10,2,-6