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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

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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?

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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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