Question

Is 38, a term of the progression −18, −14, −10, ....?

Answer 1

Yes, 38 is the 15th term of the progression

Given A.P.:

−18, −14, −10, ....

First term a = −18a

Common difference d = −14 − (−18) = 4

Formula for the nth term:

a_n = a + (n − 1)d

Assume 38 is a term of the A.P.:

−18 + (n − 1)4 = 38

−18 + 4n − 4 = 38

4n − 22 = 38

4n = 60

⇒ n = 15

Since n is a whole number, 38 is a term of the progression.