Question

For what value of k will be the consecutive terms 2k+1 ,3k+1, 5k-1 from an A.p?

Answer 1

Heya buddy !!!

Here's the answer you are looking for

To be terms of an AP, the difference of two consecutive terms should be equal to the difference of any other 2 consecutive terms.

That is , a3 - a2 = a2 - a1


Here, a3 = 5k-1

a2 = 3k+1

& a1 = 2k+1

So,

5k-1 - (3k+1) = 3k+1 - (2k+1)

5k - 1 - 3k - 1 = 3k + 1 - 2k - 1

2k - 2 = k

k = 2

Therefore, for the value of k = 2, the consecutive terms 2k+1 ,3k+1, 5k-1 from an AP.


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Answer 2

To form an AP common difference of these numbers must be equal.

ie. Common difference of t1 and t2 ;

And common difference of t2 and t3 must be equal.

Therefore,
t2 - t1 = t3 - t2

3k + 1 -( 2k + 1 ) = 5k - 1 - ( 3k + 1)

3k + 1 - 2k - 1 = 5k - 1 - 3k - 1

k = 2k - 2

k = 2.

Hence, value of k = 2.


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Hope it helps:-

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