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Question
Is 302 a term of the A.P. 3, 8, 13, ...?
Solution
3, 8, 13...
Here, we have:
a = 3
\[d = \left( 8 - 3 \right) = 5\]
\[\text { Let }a_n = 302\]
\[ \Rightarrow a + \left( n - 1 \right)d = 302\]
\[ \Rightarrow 3 + \left( n - 1 \right)5 = 302\]
\[ \Rightarrow \left( n - 1 \right)5 = 299\]
\[ \Rightarrow \left( n - 1 \right) = \frac{299}{5}\]
\[ \Rightarrow n = \frac{299}{5} + 1 = \frac{304}{5}\]
Since n is not a natural number.So, 302 is not a term of the given A.P.
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