Key Terms & Concepts
An Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
- First term (a): The initial number in the arithmetic progression.
- Common difference (d): The constant value added to each term to get the next term (can be positive, negative, or zero).
- Number of terms (n): The total count of terms in the sequence.
Key Formulas
nth Term of an AP:
an = a + (n - 1)d
Sum of First n Terms of an AP:
Sn = (n / 2) [2a + (n - 1)d]
Alternatively, when the last term l is known:
Sn = (n / 2) (a + l)
Points to Remember
Constant Difference: An AP is valid only if the difference between consecutive terms remains strictly constant throughout the sequence: d = ak+1 - ak.
Equidistant Property: The middle term of a finite AP is the average of terms that are equidistant from the beginning and the end.
Important Practice Questions
- Find the 20th term and the sum of the first 20 terms of a given AP.
- Which term of the AP 3, 8, 13, … is 78?
- Find the sum of all multiples of 7 lying between 100 and 300.
Quick Revision
General Term
an = a + (n - 1)d
Sum Formula
Sn = (n / 2)[2a + (n - 1)d]
Sum with Last Term
Sn = (n / 2)(a + l)
Common Difference
d = an - an-1