Find the value of the middle term of the following AP $- 6, - 2, 2, . . . . ., 58$

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Solution

First we will find the number of terms of the given AP,
Where, Last term $= 58$ , $a =$ first term $= - 6$
Here $d = - 2 - (- 6) = - 2 + 6 = 4$
Since, $a_{n} = a + (n - 1) d$
$\Rightarrow 58 = - 6 + (n - 1) 4$
$\Rightarrow 58 = - 6 + 4 n - 4$
$\Rightarrow 58 = - 10 + 4 n$
$\Rightarrow 58 + 10 = 4 n$
$\Rightarrow 68 = 4 n$
$∴ n = 17$
Since, number of terms is $17$ .
So middle term will be the 9th term.
We can find 9th term: $a_{9} = a + (9 - 1) \times 4$
$= - 6 + 8 \times 4$
$= 32 - 6 = 26$
So middle term of the above AP is $26$

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