The problem involves determining the number of terms in a geometric progression defined by the sequence 3, 6, 12, ..., 1536. Participants are exploring the relationship between the terms and the common ratio.
The discussion is ongoing, with some participants providing guidance on how to approach the problem by calculating powers of 2. There are also critiques of the calculations presented, indicating a lack of consensus on the correctness of the initial attempts.
Some participants note potential errors in the original poster's work and emphasize the need for proper notation in exponent expressions. There is an indication that assumptions about the geometric nature of the sequence are being questioned.
HallsofIvy said:Okay, so solve it! First, divide both sides by 3. If that sequence is actually geometric, you should be able to identify 1536/3 as a power of 2. I suggest you just calculate powers of 2: 1, 2, 4, 8, 16, ... until you get to that number.
There are errors in your work. Also, you need parentheses around your exponent expressions.nae99 said:1536= (3) (2)^n-1
1536/3 = 6^n-1[itex]/[/itex]3
512 = 2^n-1
512 = 2^10-1
512 = 2^9
n = 10
The above is incorrect. 3*2^(n - 1) [itex]\neq[/itex] 6^(n - 1)nae99 said:1536= (3) (2)^(n-1)
1536/3 = 6^n-1[itex]/[/itex]3
The above is also incorrect. [6^(n - 1)]/3 [itex]\neq[/itex] 2^(n - 1)nae99 said:512 = 2^n-1
nae99 said:512 = 2^10-1
512 = 2^9
n = 10