If the first term of the AP is a, then the second term is a+p and the 9th term is a+8p. The 19th term is a+18p and the 29th term is a+28p, where p is the constant difference between consecutive terms. If the 29th term is twice the 19th then a+28p=2(a+18p)=2a+36p, so 2a+36p-(a+28p)=0, and a+8p=0. But a+8p is the 9th term so the 9th term is zero. Therefore, if the 9th term is zero, the 29th term will be twice the 19th term.