Find the sum of the first five terms of a geometric progression if the first term is 2

Find the sum of the first five terms of a geometric progression if the first term is 2 and the denominator of the progression is 0.5.

Given: bn – geometric progression;

b1 = 2, q = 0.5;

Find: S5 -?

Formula of a geometric progression term: bn = b1 * q ^ (n – 1),

where b1 is the first term of a geometric progression, q is its denominator, n is the number of members of the progression.

According to this formula, we express the fifth term of a given geometric progression:

b5 = b1 * q ^ (5 – 1) = b1 * q ^ 4 = 2 * (0.5) ^ 4 = 0.125;

The sum of the first n members of a geometric progression is found by the formula:

Sn = bn * q – b1 / (q – 1);

Thus, substituting the known values, we get:

S5 = b5 * q – b1 / (q – 1) = 0.125 * 0.5 – 2 / (0.5 – 1) = -1.9375 / (-0.5) = 3.875.

Answer: S5 = 3.875.