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Question
Is 302 a term of the A.P. 3, 8, 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.
here we will use the formula, `a_n =a + (n - 1)d`
Here, A.P is 3, 8, 13
`a_n = 302`
a = 3
Now
Common difference (d) = `a_1 - a`
= 8 - 3
= 5
Thus, using the above mentioned formula, we get,
302 = 3 + (n -1)5
302 - 3 = 5n - 5
299 = 5n
`n = 299/5`
Since the value of n is a fraction
Thus 302 is not the term of the given A.P
Thererfore the answer is NO
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