Question

the 6th term of an Ap is zero prove that it's 31st term is five times the 11th tefm

Answer 1

given 6th term is zero
so
a + (6-1)d = 0
a + 5d = 0
so a = -5d
now
31st term is
a + (31-1)d
a + 30d..........(1)
also
11 th term is
a +(11-1)d
a + 10d
so 5 times 11 term is
5a + 50d.........(2)
on comparing with 1 we want only single a so we convert the remaining 4a into d
so
a + 4a + 50d
as
a = -5d
a + 4(-5d) + 50d
a - 20d + 50d
a + 30d
31st term

Answer 2

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