Question

In a certain A.P. the 24^th term is twice the 10^th term. Prove that the 72nd term is twice the 34th term.

Answer 1

Here, we are given that 24^th term is twice the 10^th term, for a certain A.P. Here, let us take the first term of the A.P. as a and the common difference as d

We have to prove that

So, let us first find the two terms.

As we know,

For 10^th term (n = 10),

For 24^th term (n = 24),

Now, we are given that

So, we get,

Further, we need to prove that the 72^nd term is twice of 34^th term. So let now find these two terms,

For 34^th term (n = 34),

(Using 1)

For 72^nd term (n = 72),

(Using 1)

Therefore,