Find the $n^{th}$ term of the A.P.: $11,8,5,2,$... . Write the recursive rule for this A.P.                                     [Page No. 185]

Here, $a = 11$, $d = -3$

$$n^{\text{th}} \text{ term: } a_n = 11 + (n - 1)(-3)$$

$$a_n = 11 - 3n + 3$$

$$a_n = 14 - 3n$$

Recursive rule: $a_1 = 11$

$$a_n = a_{n-1} - 3, \text{ for } n \geq 2$$

Concept Applied

The $n^{\text{th}}$ term of an AP with first term $a$ and common difference $d$ is $a_{n} = a + (n - 1)d$.