\(n^{th}\) term of an AP:
The \(n^{th}\) term \(a_{n}\) of the AP with first term 'a' and common difference 'd' is given by
\(a_{n} = a + (n – 1) d\).
\(a_{n}\) is also called the general term of the AP.
\(a_{n}\) is also called the general term of the AP.
If there are m terms in the AP, then \(a_{m}\) represents the last term which is sometimes also denoted by \(l\).
Example:
If \(a = 7\), \(d = 3\) and \(n = 8\). Find \(a_{n}\).
Solution:
\(a_{n}\) can be found using the below formula,
\(a_{n} = a + (n – 1) d\)
Substituting the known values we get,
\(a_{n} = 7 + ( 8 - 1) 3 \)
\(= 7 + (7 \times 3)\)
\(= 7 + 21\)
\(= 28\)