# Find the sum of the first eight terms of the geometric progression bn with positive terms knowing

**Find the sum of the first eight terms of the geometric progression bn with positive terms knowing that b2 = 1.2 and b4 = 4.8.**

According to the condition of the problem, a geometric progression bn is given, in which the second term is b2 = 1.2, and the fourth term is b4 = 4.8.

Using the formula for the nth term of the geometric progression bn = b1 * qn – 1, where b1 is the first term of the geometric progression, q is the denominator of the geometric progression, we can write the following ratios:

b1 * q2 – 1 = 1.2;

b1 * q4 – 1 = 4.8.

We solve the resulting system of equations.

Dividing the second equation by the first, we get:

b1 * q3 / (b1 * q) = 4.8 /1.2;

q² = 4;

q² = 2².

According to the condition of the problem, this geometric progression has positive terms, therefore, q = 2.

Substituting the found value of q into the ratio b1 * q = 1.2, we obtain;

b1 * 2 = 1.2;

b1 = 1.2 / 2;

b1 = 0.6.

Using the formula for the sum of the first n terms of the geometric progression Sn = b1 * (1 – qⁿ) / (1 – q) for n = 8, we find the sum of the first eight members of this geometric progression:

S8 = 0.6 * (1 – 28) / (1 – 2) = 0.6 * (1 – 256) / (-1) = 0.6 * 255 = 153.

Answer: the sum of the first eight members of this geometric progression is 153.