Question

Find fout consecutive terms of an A.P. such that the difference of the middle terms is 8 and the product of extreme terms is 217.

Answer 1

Let the terms be
a, a+d, a+2d, a+3d

a+2d-a -d= 8
d= 8
(a)(a+3d)= 217

a² + 3ad =217
a²+24a -217=0
a² - 31a +7a -217= 0
a(a-31) +7 (a-31)=0
a= -7, 31
so a=31