Arithmetic Progression (AP)
- Formula / Rule
- Arithmetic Progression (AP)
- Topic
- Sequences & Series
- Formula
nth term: $a_n = a + (n-1)d$
Sum of n terms: $S_n = \frac{n}{2} \times [2a + (n-1)d]$ or $S_n = \frac{n}{2} \times (\text{first term} + \text{last term})$
Where:
- $a$ = first term
- $d$ = common difference
- $n$ = number of terms
- When to Use
- Number series with constant difference; sum of natural numbers, odd/even numbers.
- Worked Example
Q: Find the 10th term of AP: 3, 7, 11, 15...
$d = 4, a = 3$ $a_{10} = 3 + (10-1) \times 4 = 3 + 36 = \textbf{39}$