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

Answer Details

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.