Given a geometric progression 1: 2: 4 find the 8th member of the progression.

Let’s find what the denominator of this geometric progression is equal to.
The statement of the problem says that the number that is in this sequence at position number one is 1, and the number that is in this sequence at position number two is 2.
Using the definition of a geometric progression, we find the denominator q of this progression:
q = b2 / b1 = 2/1 = 2.
Using the formula of the geometric progression term, which stands at the n-th position bn = b1 * q ^ (n – 1) for n = 8, we find the 8th term of this progression:
b8 = 1 * 2 ^ (8 – 1) = 2 ^ 7 = 128.
Answer: The 8th term of this progression is 128.