Indicate the first three terms of the arithmetic progression if a1 = 0.5 d = 1.5

Given: (an) – arithmetic progression;

a1 = 0.5; d = 1.5;

Find: a1, a2, a3 -?

The formula for the n-th member of the arithmetic progression:

an = a1 + d (n – 1),

where a1 is the first term of the progression, d is the difference of the progression, n is the number of its members.

Using this formula, we write down the second and third terms of the given progression:

a2 = a1 + d (2 – 1) = a1 + d;

a3 = a1 + d (3 – 1) = a1 + 2d.

Substitute the known values of the first term and the difference and find the required terms of the progression:

a2 = a1 + d = 0.5 + 1.5 = 2;

a3 = a1 + 2d = 0.5 + 2 * 1.5 = 3.5.

Answer: a1 = 0.5; a2 = 2; a3 = 3.5.