The general form of an A.P is: $(a,a + d,a + 2d,a + 3d....)$ where a is the first term and d is a common difference. Here, $d = 0$ or $d > 0$ , or $d < 0$

The nth term of an AP

The nth term of an A.P is given by $Tn = a + (n - 1)d$ , where a is the first term, d is a common difference and n is the number of terms.

Example

Find the 11th term of the AP: 23, 19, 15,…

Solution

Given a = 23, n = 11, d = 19 – 23 = – 4

$\begin{array}{l}{a_n} = a + (n - 1)d\\{a_{11}} = 23 + (11 - 1) - 4\\ = 23 + (10) - 4\\ = 23 - 40\\ = - 17\end{array}$

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