Given:
- The first term of the arithmetic progression (AP) is 100.
- The last term of the AP is 1000.
- The sum of a certain number of terms in the AP is 5500.

To Find:
- The number of terms in the AP.

Formula:
The sum of an AP can be calculated using the formula:
Sn = (n/2) * (a + l)
where:
- Sn is the sum of the AP
- n is the number of terms in the AP
- a is the first term of the AP
- l is the last term of the AP

Solution:
- We are given that the first term (a) is 100 and the last term (l) is 1000.
- We are also given that the sum of a certain number of terms (Sn) is 5500.

Step 1: Calculate the common difference (d)
To find the common difference (d) in an AP, we can use the formula:
d = (l - a)/(n - 1)
where:
- d is the common difference
- l is the last term of the AP
- a is the first term of the AP
- n is the number of terms in the AP

In this case, substituting the given values:
d = (1000 - 100)/(n - 1)
d = 900/(n - 1)

Step 2: Calculate the sum of the AP (Sn)
Using the formula for the sum of an AP:
Sn = (n/2) * (a + l)
Substituting the given values:
5500 = (n/2) * (100 + 1000)
5500 = (n/2) * 1100
5500 = 550n
n = 5500/550
n = 10

Step 3: Calculate the common difference (d)
Substituting the value of n into the formula for the common difference:
d = 900/(10 - 1)
d = 900/9
d = 100

Step 4: Calculate the sum of the AP (Sn)
Using the formula for the sum of an AP:
Sn = (n/2) * (a + l)
Substituting the given values:
5500 = (10/2) * (100 + 1000)
5500 = 5 * 1100
5500 = 5500

Step 5: Conclusion
The number of terms in the AP is 10.