Find $n$ if the given value of $x$ is the $n$ th term of the given A.P.
$- 1, - 3, - 5, - 7, . . . .; x = - 151$

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Solution

Given sequence is $- 1, - 3, - 5, - 7, . . .$

The first term $a = - 1$ and

the common difference $d = - 3 - (- 1) = - 2$

Given that the $n^{t h}$ term is $- 151$

We know that the $n^{t h}$ term of the arithmetic progression is given by $a + (n - 1) d$

Therefore, $a + (n - 1) d = - 151$

$⟹ - 1 + (n - 1) * (- 2) = - 151$

$⟹ - 1 + 2 - 2 n = - 151$

$⟹ 1 - 2 n = - 151$

$⟹ 2 n = 152$

$⟹ n = \frac{152}{2}$

$⟹ n = 76$

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Find $n$ if the given value of $x$ is the $n$ th term of the given A.P.
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