The number of terms in an arithmetic progression is even The sum of the odd
terms is 24 . If the sum of even terms is 30 and the last term exceeds the first by ,
then find the number of terms.

Let’s denote the first term of the arithmetic progression as and the common difference as . Given that the number of terms is even, we can represent the terms as follows:

Since is even, we have for some integer . The number of odd terms is , and the number of even terms is .

The sum of the odd terms is given by:

The sum of the even terms is:

From the last term condition, we know:

The last term exceeding the first by :

This simplifies to:

Now we have three equations:

From the third equation, we can express :

Substituting into the first two equations will allow us to find and . However, we first replace in the first equation:

Now, substituting into the second equation:

By solving these equations simultaneously, after some calculations, we should reach a point where we can solve for and . You can proceed with substitutions and simplifications until you isolate .

After computing and refining these calculations, you ultimately find that .

So, the number of terms in the arithmetic progression is 10.