So i have to find the first 5 terms of each sequence; 2^x-1. Would I start at 0? I mean is 0 a natural number
if x refers to the term number, then it must be a natural number. The first of the natural numbers, sometimes called the counting numbers, is 1
term(x) = 2^x - 1
term(1) = 2^1 - 1 = 1
term(2) = 2^2 - 1 = 4-1 = 3
term(3) = 2^3 - 1 = 8-1 = 7
etc.
Wow...
To find the first 5 terms of the sequence 2^x - 1, you would start by substituting different values for x, starting from an initial value. Whether or not to include 0 as a natural number depends on the definition being used.
In mathematics, there are different definitions for natural numbers. The most common definitions include either starting from 1 or 0.
If you are using the definition that includes 0 as a natural number, then you would start at x = 0 and substitute it into the sequence formula:
2^0 - 1 = 1 - 1 = 0. So, the first term of the sequence would be 0.
If you are using the definition that excludes 0 from natural numbers, then you would start at x = 1 and substitute it into the sequence formula:
2^1 - 1 = 2 - 1 = 1. So, the first term of the sequence would be 1.
After finding the first term, you would increment the value of x by 1 and substitute again to find the subsequent terms. Repeat this process until you have found the first 5 terms of the sequence.