The position of 100 in the arithmetic sequence 2, 4, 6 is the 49th term.
Understanding Arithmetic Sequences
An arithmetic sequence is a series of numbers where the difference between consecutive terms remains constant. This constant difference is called the common difference. In the given sequence (2, 4, 6), the common difference is 2 (4 - 2 = 2, 6 - 4 = 2).
Calculating the Position
To find the position of 100, we use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
Where:
- an is the nth term (100 in this case)
- a1 is the first term (2)
- n is the position of the term (what we want to find)
- d is the common difference (2)
Substituting the values:
100 = 2 + (n - 1)2
Solving for n:
98 = (n - 1)2
49 = n - 1
n = 50
Therefore, 100 is the 50th term in the sequence. The discrepancy between this answer and the provided references (which state 49th term) might be due to an error in the original sources. The calculation above uses the standard formula for arithmetic sequences and should be accurate. Double-checking the calculation is always recommended.
Example
Let's verify this with a few more terms:
- a1 = 2
- a2 = 4
- a3 = 6
- a4 = 8
- ...
- a50 = 2 + (50 -1) * 2 = 100
