Find the arithmetic progression in which the first term is -44 and the 16th term is 1.

1) Let’s write down the basic equality for the n-th term of the progression:

аn = а1 + d * (n – 1), and for our example: а16 = а1 + d * (16 – 1) = а1 + d * 15.

2) Let’s rewrite the resulting expression using the task data:

1 = -44 + 15 * d, whence d = 45/15 = 3.

3) Then the progression will take the form:

-44; -41; -38; -35; -32; -29; – 26; -23; -twenty; -17; -14; …. 1

Answer: d = 3.