How i solve this optional chapter of arithmetic progressions of class 10th math it is very important of question, please suggest me the best way to solve this question Which term of the AP: 121, 117, 113, . . ., is its first negative term? [Hint: Find n for an < 0]

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

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Given the AP series is 121, 117, 113, . . .,

Thus, first term, a = 121

Common difference, d = 117-121= -4

By the nth term formula,

a=_{n}a+(n−1)dTherefore,a

_{n}= 121+(n−1)(-4)= 121-4n+4

=125-4n

To find the first negative term of the series,

a< 0_{n }Therefore,

125-4n < 0

125 < 4n

n>125/4

n>31.25

Therefore,the first negative term of the series is 32^{nd}term.