Question

if the sum of three 3 numbers in ap is 30 and the product of first and last term is 216 then find numbers​

Answer 1

Step-by-step explanation:

let the AP be a-d, a, a+d

sum of the 3 numbers = 30

a - d + a + a + d = 30

3a = 30

a = 30/3

a = 10

product of first and last term = 216

(a - d) (a + d) = 216

${a}^{2} - {d}^{2} = 216 \\ {10}^{2} - {d}^{2} = 216 \\ 100 - {d}^{2} = 216 \\ - {d}^{2} = 216 - 100 \\ - {d}^{2} = 116 \\ - d = \sqrt{116} \\ - d = 10.71 \\ d = - 10.71$

therefore the numbers are

a - d = 10 - (-10.71) = 10 + 10.71 = 20.71

a = 10

a + d = 10 + (-10.71) = 10 - 10.71 = - 0.71

the AP is

20.71, 10, - 0.71

hope you get your answer