MATH SOLVE

5 months ago

Q:
# Calculates the product of the first eight terms of GP (1/8,1/4,1/2,...)

Accepted Solution

A:

To calculate the product of the first eight terms of the geometric progression (GP) with the initial term 1/8 and a common ratio of 2, you can use the formula for the nth term of a geometric progression:
a_n = a_1 * r^(n-1)
In this case, a_1 = 1/8 and r = 2. We want to find the product of the first eight terms, which means n = 8.
So, for the first eight terms:
a_1 = 1/8
a_2 = a_1 * r = (1/8) * 2 = 1/4
a_3 = a_1 * r^2 = (1/8) * 2^2 = 1/2
a_4 = a_1 * r^3 = (1/8) * 2^3 = 1
a_5 = a_1 * r^4 = (1/8) * 2^4 = 2
a_6 = a_1 * r^5 = (1/8) * 2^5 = 4
a_7 = a_1 * r^6 = (1/8) * 2^6 = 8
a_8 = a_1 * r^7 = (1/8) * 2^7 = 16
Now, to find the product of these eight terms, you simply multiply them together:
Product = (1/8) * (1/4) * (1/2) * 1 * 2 * 4 * 8 * 16
Product = (1/8) * (1/4) * (1/2) * 1 * 2 * 4 * 8 * 16
Now, multiply the numbers together:
Product = (1/8) * (1/4) * (1/2) * 1 * 2 * 4 * 8 * 16 = 16
So, the product of the first eight terms of the given geometric progression is 16.