In the sequence 2,6,10....what term has a value of 106?
That's a pretty small sample, but it appears that
Tn = 2*(nth odd number)
So, 106 = 2*53
53 is the 27th odd number
To find the term in a sequence that has a specific value, we need to determine the pattern or rule of the sequence. In this case, the sequence seems to be increasing by 4 with each term.
To confirm this pattern, we can subtract consecutive terms and check if the difference is always the same. Let's try:
6 - 2 = 4
10 - 6 = 4
Since the difference between consecutive terms is always 4, we can say that the rule of this sequence is to add 4 to each term. The formula for this sequence can be written as:
An = A1 + (n - 1) * d
Where:
An represents the nth term of the sequence
A1 is the first term
n is the position of the term in the sequence
d is the common difference (which is 4 in this case)
Now, we can solve the equation for the given value, 106:
106 = 2 + (n - 1) * 4
Subtract 2 from both sides of the equation:
104 = (n - 1) * 4
Divide both sides of the equation by 4:
26 = n - 1
Add 1 to both sides of the equation:
n = 26 + 1
n = 27
Therefore, the term that has a value of 106 in this sequence is the 27th term.