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Question
Which term of the A.P. 84, 80, 76, ... is 0?
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Solution
84, 80, 76...
Here, we have:
a = 84
\[d = \left( 80 - 84 \right) = - 4\]
\[\text { Let }a_n = 0\]
\[ \Rightarrow a + (n - 1)d = 0\]
\[ \Rightarrow 84 + (n - 1)\left( - 4 \right) = 0\]
\[ \Rightarrow (n - 1)\left( - 4 \right) = - 84\]
\[ \Rightarrow (n - 1) = 21\]
\[ \Rightarrow n = 22\]
Hence, 0 is the 22nd term of the given A.P.
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