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Question
Find Is 68 a term of the A.P. 7, 10, 13, ...?
Solution
In the given problem, we are given an A.P and the value of one of its term.
We need to find whether it is a term of the A.P or not.
So here we will use the formula, `a_n = a + (n - 1)d`
Here, A.P is 7, 10, 13
`a_n = 68`
a = 7
Now
Common difference (d) = `a_1 - a`
= 10 - 7
= 3
Thus using the above mentioned formula we get
`68 = 7 + (n - 1)3`
68 - 7 = 3n - 3
61 +3 = 3n
`n = 64/3`
Since the value of n is a fraction
Thus 68 is not the term of the given A.P
Therefore the answer is NO
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