Is there an arithmetic progression in which A7 = -67, A13 = -19, and A45 = 133?

Let’s calculate what value the difference of the progression should take, in which, in accordance with the available data in the conditions of our task, the seventh element is -67, and the thirteenth is -19:

d = (-19 – (-67)): (13 – 7) = 8.

Let’s find out what value the difference of the progression should take, in which, in accordance with the available data under the conditions, the seventh element is -67, and the forty-fifth is 133:

d = (133 – (-67)): (45 – 7) = 200: 38 = 5 and 10/38.

Let’s compare:

8> 5 and 10/38.

Answer: No.