Question

If 9th term of an ap is zero prove that its 29th term is double the 19th term

Answer 1

Answer:

given

a+8d=0

a=-8d.

where a is the first term and d is the common difference

then 19th term =a+18d

=-8d+18d

=10d

29th term

a+28d

=-8d+28d

=20d

therefore 29th term=2×19th term

i.e.20d=2×10d

Answer 2

Given:-

• 9th term of an ap is zero

Prove that:-

• Its 29th term is double the 19th term.?

Proof:-

• Let the first term of the A.p as a and common difference as d.

We know that:-

• an = a + (n - 1)d

The 9th term of an Ap is zero.

=> a9 = a + (9 - 1)d

=> 0 = a + 8d

=> a = -8d .........(1).

Now, The 29th term is double of 19th term.

For 19th term.

=> a19 = a + (19 - 1)d

=> a19 = -8d + 18d (using Eq. 1)

=> a19 = 10d

For 29th term.

=> a29 = a + (29 - 1)d

=> a29 = -8d + 28d (using Eq. 1)

=> a29 = 20d

=> a29 = 2 × 10d

=> a29 = 2 × a19

Therefore Ap the 29th term is double of the 19th term.

Hence, proved.