Find the difference and the eleventh term of the arithmetic progression 3; 7; 11; 15.

We are given an arithmetic progression (an) by its first, second, third and fourth terms 3; 7; eleven; fifteen; ….

In order to find the difference of the arithmetic progression, let’s remember the formula for finding it:

d = an + 1 – an;

d = a2 – a1;

Substitute and calculate:

d = 7 – 3 = 4;

To find the eleventh term of an arithmetic progression, recall the formula for finding the nth term of the progression.

an = a1 + d (n – 1);

a11 = a1 + d (11 – 1);

We substitute the value of the first term and the difference of the progression and calculate:

a11 = 3 + 4 (11 – 1) = 3 + 4 * 10 = 3 + 40 = 43.