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# Which term of the AP : 121, 117, 113, . . ., is its first negative term?

Q : 1     Which term of the AP :  $\small 121,117,113,...,$ is its first negative term?  [Hint : Find $n$ for $a_n<0$ ]

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Given AP is
$\small 121,117,113,...,$
Here $a = 121 \ and \ d = -4$
Let suppose nth term of the AP is first negative term
Then,
$a_n = a+ (n-1)d$
If nth term is negative then $a_n < 0$
$\Rightarrow 121+(n-1)(-4) < 0$
$\Rightarrow 125<4n$
$\Rightarrow n > \frac{125}{4}=31.25$
Therefore, first negative term must be 32nd term

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