Question

If 9th term of an arithmetic progression is 0, prove that its 29th term is double the 19th term.

Answer 1

If the 9th term of an AP is 0 , then
a+8d = 0
a = -8d

29th term = a + 28d
= -8d + 28d = 20d

19th term = a +18d
= -8d + 18d = 10d

since 20d = 2(10d)
the 29th term is twice the 19th term