Question

the sum of the first three terms of an AP is 3 and the product of first and third term is -35

Answer 1

Answer:

the AP is

-5, 1, 7

Step-by-step explanation:

let the numbers in AP is a-d, a, a+d

sum of the three terms is 3

a - d + a + a + d = 3

3a = 3

a = 3/3 = 1

product of first and third term is = -35

(a - d)(a + d) = - 35

${a}^{2} - {d}^{2} = - 35 \\ {1}^{2} - {d}^{2} = - 35 \\ - {d}^{2} = - 35 - 1 \\ - {d}^{2} = - 36 \\ {d}^{2} = 36 \\ d = \sqrt{36} \\ d = 6$

therefore the numbers are

a - d = 1 - 6 = -5

a = 1

a + d = 1 + 6 = 7

the AP is

-5, 1, 7