Step-by-step explanation:
Let the three consecutive terms in AP a - d, a, &.
a + d
[tex] \therefore \: a - d + a + a + d = 15 \\ \therefore \:3 a = 15 \\ \therefore \: a = \frac{15}{3} \\ \therefore \: a = 5 \\ \\ \because (a - d ) \times a \times ( a + d ) = 100 \\ \therefore \: a ( {a}^{2} - {d}^{2} ) = 100 \\ \therefore \: 5 ( {a}^{2} - {d}^{2} ) = 100\\ \therefore \: ( {a}^{2} - {d}^{2} ) = \frac{100}{5} \\ \therefore \: ( {5}^{2} - {d}^{2} ) = 20 \\ \therefore \: 25 - {d}^{2} = 20 \\ \therefore \: 25 - 20 = {d}^{2} \\ \therefore \:{d}^{2} = 5 \\ \therefore \:{d} = \pm\sqrt{5} \\ \\ thus \: first \: term \: (a) = 5 \\ common \: difference \: (d)= \pm\sqrt{5} [/tex]
