The general form of an AP

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 = 0ord > 0, or  d < 0

The nth term of an AP

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