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Question
Is 68 a term of the A.P. 7, 10, 13, ...?
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Solution
7, 10, 13...
Here, we have:
a = 7
\[d = \left( 10 - 7 \right) = 3\]
\[\text { Let } a_n = 68\]
\[ \Rightarrow a + (n - 1) d = 68\]
\[ \Rightarrow 7 + (n - 1)(3) = 68\]
\[ \Rightarrow (n - 1)(3) = 61\]
\[ \Rightarrow (n - 1) = \frac{61}{3}\]
\[ \Rightarrow n = \frac{61}{3} + 1 = \frac{64}{3}\]
Since n is not a natural number.So, 68 is not a term of the given A.P.
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