Question

What is the value of k will. Be consecutive terme 2k + 1, 3k +3and 5 k- 1 from an AP

Answer 1

Hi
Nice question

Question:-
What is the value of k if 2k + 1, 3k + 3 and 5k - 1 are the consecutive terms of A.P. ?

Solution:-

If these terms are the consecutive terms , then their common difference (d) will also be same.

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

3k + 3 - 2k - 1 = 5k - 1 - 3k - 3
k + 2 = 2k - 4
k - 2k = - 4 - 2
-k = -6
k = 6

Hope this helps you.

Answer 2

As it a AP , Com on difference will be equal between every consecutive terms...

Common difference between a3 and a2 = Common difference between a2 and a1

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

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

2k - 4 = k + 2

k = 6