Question

if for an a.p. a5 = a10 = 5a ,then a15 is..

Answer 1

a5 = a10 = 5×a
so,
a+4d = a+9d= 5a
so, 5a=a+4d (first case)
5a-a=4d
4a=4d
a=d
and, so , a15=a+14d
= a+14a
=15a
and , 5a=a+9d
4a=9d
d=4\9a
so, a15=a+14d
= a+ 14 × 4\9a
=a+ 56a\9
=(8a+56a)\9
=(64a)\9
=7.1 a
which cannot be true for a single a.p unless d=0 ,so, the question is wrong .

Answer 2

Answer

a5 = a10 = 5a

=》 a5 = 5a

a + 4d = 5a

a = d

=》 a10 = 5a

a + 9d = 5a

9d = 4a

9d = 4d

d = 0

=》 a15 = a + 14d

= a + 14 (0)

= 0 + 0

= 0