Question

If the sum of three consecutive terms of an AP is 15 and

their product is 100. What is the first
he common diffrences

Answer 1

Explanation:

Let the three consecutive terms in AP a - d, a, &.

a + d

`\therefore \: a - d + a + a + d = 15 \\ \therefore \:3 a = 15 \\ \therefore \: a = (15)/(3) \\ \therefore \: a = 5 \\ \\ \because (a - d ) * a * ( a + d ) = 100 \\ \therefore \: a ( {a}^(2) - {d}^(2) ) = 100 \\ \therefore \: 5 ( {a}^(2) - {d}^(2) ) = 100\\ \therefore \: ( {a}^(2) - {d}^(2) ) = (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√(5) \\ \\ thus \: first \: term \: (a) = 5 \\ common \: difference \: (d)= \pm√(5)`

Answer 2

Answer:common difference is 2.24

Explanation: