Question

If 9th term of an AP is 0 prove that its 29th term is double of its 19 term

Answer 1

let a be the first term of AP and d be the difference. Then we know that nth term of AP will be
nth term = a + (n -1)d
so the 9th term will be
9th term = a + (9 -1)d = 0 (given)
a + 8d = 0
a = -8d
Now the 19th term will be
19th term = a + 18d
putting the value of a
19th term = -8d + 18d
= 10d
and the 29th term will be
29th term = a + 28d
putting the value of a
29th term = -8d + 28d
= 20d
so the 29th term is 20d which is double of 19th term= 10d. Proved

Answer 2

commen difference be d
a9=a=(9-1)d
     =a+8d
 a=-8d
a29=a+(29-1)d
       =-8a+28d
20d=2*10d
      =2(-8a+28d)
      =2(a+18d)
       =2*29th term
thus 29th term is double of its 19th term.