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# In a Certain A.P. the 24th Term is Twice the 10th Term. Prove that the 72nd Term is Twice the 34th Term. - CBSE Class 10 - Mathematics

#### Question

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

#### Solution

Here, we are given that 24th term is twice the 10th 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 a_72 = 2a_34

So, let us first find the two terms.

As we know

a_n = a + (n - 1)d

For 10th term (n = 10)

a_10 = a + (10 - 1)d

= a + 9d

For 24 th term (n = 24)

a_24 = a + (24 - 1)d

= a + 23d

Now we given that a_24 = 2a_10

So we get

a + 23d = 2(a + 9d)

a + 23d = 2a + 18d

23d - 18d = 2a - a

5d = a .....(1)

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

For 34th term (n = 34),

a_34 = a + (34 - 1)d

= 5d + 33d  (Using 1)

= 38d

For 72nd term (n = 72)

a_72 = a + (72 - 1)d

= 5d + 71d     (using 1)

= 76d

= 2(38d)

Therefore a_72 = 2a_34

Is there an error in this question or solution?

#### APPEARS IN

Solution In a Certain A.P. the 24th Term is Twice the 10th Term. Prove that the 72nd Term is Twice the 34th Term. Concept: nth Term of an AP.
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