Question

If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.

Answer 1

Step-by-step explanation:

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

=a+8d

a+8d=0

=>a=-8d .....(i)

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

= a+28d

=-8d+28d ......(using (i))

=20d

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

= a+18d

= -8d+18d ......(using (i))

= 10d

19th term=10d

19th term *2=10d*2

=20d

=29th term (PROVED)

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)