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Answer :

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

Thus, first term, a = 121

Common difference, d = 117-121= -4

By the \(n^{th}\) term formula,

\(a_n = a+(n -1)d\)

Therefore,

\(a_n = 121+(n-1)(-4)\)

= 121-4n+4

=125-4n

To find the first negative term of the series, \(a_n < 0\)

Therefore,

\(\Rightarrow \) 125-4n < 0

\(\Rightarrow \) 125 < 4n

\(\Rightarrow \) n>125/4

\(\Rightarrow \) n>31.25

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

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