Question

Is 303, a term of the progression 5, 10, 15, ...?

Answer 1

No, 303 is not a term of the progression.

The given sequence is 5, 10, 15,…

a = 5

d = 10 − 5

= 5

This is an Arithmetic Progression consisting entirely of multiples of 5.

For any number to be a term in this progression, it must satisfy the general term formula a_n = a + (n − 1), where n is a positive integer.

303 = 5 + (n − 1)5

298 = (n − 1)5

n − 1 = 59.6

n = 60.6

Since n is not a whole number, 303 is not a term. The closest terms are the 60th term (300) and the 61st term (305).