A sequence is given by \(2\frac{1}{2}, 5, 7\frac{1}{2}, .....\) if the nth term is 25, find n

The given sequence is an arithmetic sequence, because the difference between consecutive terms is constant. To find the common difference d, we subtract the second term from the first term:

5 - 2.5 = 2.5

So the common difference is 2.5. We can use this common difference to find any term of the sequence, using the formula:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

We know that the nth term is 25, so we can set an = 25 and solve for n:

25 = 2.5 + (n - 1)2.5

Simplifying the equation, we get:

22.5 = 2.5n - 2.5
25 = 2.5n
n = 10

Therefore, the term number n for which the nth term of the sequence is 25 is 10, which corresponds to.

Therefore, the correct answer is: 10.