The 1st four terms of Arithmetic Progression:
a1, a1+d, a1+2d, a1+3d
The Geometric Progression:
a1+4, a1+d+2, a1+2d+5, a1+3d+18
From the GP:
a1+d+2a1+4=a1+2d+5a1+d+2=a1+3d+18a1+2d+5
a1+d+2a1+4=a1+2d+5a1+d+2
(a1+d+2)2=(a1+4)(a1+2d+5)
a12+d2+4+2a1d+4a1+4d=a12+2a1d+5a1+4a1+8d+20
d2−4d−5a1=16 ← Equation (1)
a1+2d+5a1+d+2=a1+3d+18a1+2d+5
(a1+2d+5)2=(a1+d+2)(a1+3d+18)
a12+4d2+25+4a1d+10a1+20d=a12+4a1d+20a1+3d2+24d+36
d2−4d−10a1=11 ← Equation (2)
Equation (1) - Equation (2):
5a1=5
a1=1
From Equation (1):
d2−4d−21=0
d=7 and −3 answer