Question

A geometric progression has eight terms. Its first and last term are 0.3 and 38.4 . Calculate
The common ratio
The sum of the term of the G.P

Answer 1

To find the common ratio of the geometric progression, we can use the formula:

last term = first term * (common ratio)^(number of terms - 1)

Plugging in the given values, we have:

38.4 = 0.3 * (common ratio)^(8-1)

Simplifying this equation, we get:

common ratio^7 = (38.4 / 0.3) = 128

Taking the seventh root of both sides, we find:

common ratio = ∛(128) ≈ 2

So the common ratio is 2.

To find the sum of the terms of the geometric progression, we can use the formula:

sum = (first term * (1 - (common ratio)^number of terms)) / (1 - common ratio)

Plugging in the given values, we have:

sum = (0.3 * (1 - (2^8))) / (1 - 2)

Simplifying this equation, we get:

sum = (0.3 * (1 - 256)) / (-1)

sum = (0.3 * (-255)) / (-1)

sum ≈ 76.5

So the sum of the terms of the geometric progression is approximately 76.5.