Question

Is 302 a term of the AP :3,8,13.....?

Answer 1

3,8,13...
common difference, d = 5
first term, a = 3
An = a + (n-1)*d
If An = 302,
302 = 3 + (n-1)*5
302-3 = (n-1)*5
299 = (n-1)*5
Since 299 is not exactly divisible b '5', 302 can't be a term of the given A.P

Answer 2

Given AP,
3,8, 13,....
Where common difference(d) is 5
First term(a) is 3
To check whether 302 is a term of the given AP, let's assume that it's a term in the given AP.
T(n) = a +(n-1)d
302 = 3+ (n-1)5
302 = 3+ 5n -5
302 = 5n -2
304 = 5n
304 is not perfectly divisible by 5.
So 302 is a term of the given AP.