Question

if 9th term of an AP is zero , prove that its 29th term is double the 19th term ?

Answer 1

hey mate,
here, a+8d=0
Now, a= -8d .......(1)
we have,
a+28d, from eqn 1,
we have.. -8d+28d = 20d ......(2)
now, a+18d, from eqn 1,
-8d+18d=10d .......(3)
so, on comparing..
2(19th term ) = (29th term )
Qed.

HOPE IT HELPS..

Answer 2

Question:-

➡ If the 9th term of an A.P. is zero then prove that, 29th term is twice the 19th term.

Proof:-

Let us assume that,

➡ First term of the A.P. = a and,

➡ Common Difference = d

Now,

Nth term of an A.P. = a + (n -1)d

So,

9th term = a + (9 - 1)d

= a + 8d

Now, it's given that, 9th term of the A.P. is zero.

➡ a + 8d = 0 .....(i)

Now,

29th term = a + (29 - 1)d

= a + 28d

19th term = a + (19 - 1)d

= a + 18d

Now,

29th term - 2 × 19th term

= a + 28d - 2 × (a + 18d)

= a + 28d - 2a - 36d

= -a - 8d

= -1(a + 8d)

= -1 × 0

= 0

Hence,

29th term - 2 × 19th term = 0

➡ 29th term = 2 × 19th term. (Hence Proved)