let the terms of the A.P. be

a1

a2 = a1 + d

a3 = a1 + 2d

a4 = a1 + 3d

a5 = a1 + 4d

the sum of the 5 consecutive terms is

S5 = (5/2)(a1 + a5)

120 = (5/2)(a1 + a1 + 4d)

5(a1 + 2d) = 120

a1 + 2d = 24

a1 = 24 - 2d

the ratio of the product of the first n d last terms to the product of 2nd n 4th term is 20:21

(a1*a5) : (a2*a4) = 20 : 21

21a1(a1 + 4d) = 20(a1 + d)(a1 + 3d)

plug a1 = 24 - 2d into the last equaton

21(24 - 2d )(24 - 2d + 4d) = 20(24 - 2d + d)(24 - 2d + 3d)

by solving we find 2 solutions

d1 = 3

d2 = -3

click here to see the step by step solution of the equation

Click to see all the steps

for d1 = 3 we have a1 = 24 - 6 = 18 thus the terms are

18, 21, 24, 27, 30

for d1 = -3 we have a1 = 24 + 6 = 30 thus the terms are

30, 27, 24, 21, 18