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Question
Which term of the A.P. 4, 9, 14, ... is 254?
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Solution
4, 9, 14...
Here, we have:
a = 4
\[d = \left( 9 - 4 \right) = 5\]
\[\text { Let } a_n = 254\]
\[ \Rightarrow a + \left( n - 1 \right) d = 254\]
\[ \Rightarrow 4 + \left( n - 1 \right) 5 = 254\]
\[ \Rightarrow \left( n - 1 \right) 5 = 250\]
\[ \Rightarrow \left( n - 1 \right) = 50\]
\[ \Rightarrow n = 51\]
Hence, 254 is the 51st term of the given A.P.
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