Are the numbers A = 48 and B = -128 members of the arithmetic progression (An) if An = 2-8n?

To find whether the numbers a = 48 and b = -128 are members of the arithmetic progression (an), if the arithmetic progression is given by the nth term of the arithmetic progression an = 2 – 8n.

In other words, if the given numbers are members of an arithmetic progression, we must find their number.

To do this, we will solve two linear equations.

a = 48;

48 = 2 – 8n;

8n = 2 – 48;

8n = -46;

n = -46: 8;

n = -5.75.

the number a is not a member of this progression.

b = -128;

-128 = 2 – 8n;

8n = 2 + 128;

8n = 130;

n = 130: 8;

n = 16.25

they are also not a member of the progression.