kevincan wrote:

We know that each term is either 5,6 or 7 greater than the previous term

Why not 4.5, 5.5, 6.5, 7.7 ..... The question doesnt say that it has to be greater by an integral value.

kevincan wrote:

Thus 5(k-1) is less than or equal to ak - (-30) which is less than or equal to 7(k-1)

We know that ak = 47

Thus 7(k-1) >= 77 i.e. k is greater than or equal to 12

5(k - 1) <= 77 i.e k is less than or equal to 16

Thus k can be either 12, 13, 14, 15, 16

If you use difference as 7.7, then k can be 11. Similarly other values of k possible. As solved in my earlier post, there can be a total of 10 values.

kevincan wrote:

Thanks for all who tried. I hope we see that not all sequences are AP, GP

But this sequence is. In fact, indirectly you yourself have used the formulas that are typical of APs.