Q. 224.7( 9 Votes )

Is 184 a term of the AP 3, 7, 11, 15, ...?

Answer :

Here, First term = a = 3

Common difference = d = 7 - 3 = 4


Now, to check: 184 is a term of the AP or not.


Since, nth term of an AP is given by:


an = a + (n - 1)d


If 184 is a term of the AP, then it must satisfy this equation.


So, let an = 184


184 = 3 + (n - 1) × 4


184 - 3 = 4n - 4


181 = 4n - 4


181 + 4 = 4n


4n = 185


n = 185/4 = 46.25


But this is not possible because n is the number of terms which can’t be a fraction.


Therefore, 184 is not a term of the given AP.


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