Question

Q1. Find the four consecutive terms such that the sum of the middle two terms is 18
and the product of the two end terms is 45​

Answer 1

let terms be X, X + 1 , X + 2, X + 3.

x+1 + x+2 = 18

2x = 6

x=3

and

x*x+3 = 45

x^2= 42

Answer 2

Step-by-step explanation:

Let the four consecutive numbers be x, x+d,

x+2d, and x+3d

Given,

sum of middle two terms is 18

i.e. (x+d) + (x+2d) = 18

2x + 3d = 18

3d = 18-2x. ...(1)

product of the two end terms is 45

i.e. X(X+3d) = 45

x(x+18-2x) = 45. from (1)

x(18-x) = 45

x²-18x = 45

x²-18x+45 = 0

x²-15x-3x+45 = 0

x(x-15)-3(x-15) = 0

x-3 = 0 or x-15 = 0

x=3 or x= 15

Taking 3 in terms of x in,

2x+3d = 18

2(3)+3d = 18

6+3d=18

3d=12

d=4

Therefore, the terms are x=3, x+d =3+4= 7,

x+2d=3+2(4)=11 and x+3d=3+3(4)=15

i.e. the terms are 3,7,11 and 15.