Find the common difference and a formula formula for the nth term of the arithmetic sequence; 6, 2, -2, -6, -10,...a sub n =
a)6-4n
b)6-2n
c)10-2n
d)10-4n
I think it is c but want to check.
Ao is 10, then each term subtracts 4n from it....n=1, ...
well if 6 is equal to the first term of the sequesnce the only one that would work would be d.
1st = 6 so 10-4(1)=6 where n is the number of the term
2nd = 2 so 10-4(2)=2
3rd term = -2 so 10-4(3)=-2
Hope that helped.
To find the common difference and the formula for the nth term of an arithmetic sequence, you need to look for the pattern in the given sequence.
The arithmetic sequence is: 6, 2, -2, -6, -10,...
First, let's find the common difference:
To find the common difference, you subtract any term from its previous term.
2 - 6 = -4
-2 - 2 = -4
-6 - (-2) = -4
-10 - (-6) = -4
...
As you can see, the common difference is -4.
Now, let's find the formula for the nth term:
The formula for the nth term of an arithmetic sequence is given by: a sub n = a sub 1 + (n-1)d
Here, a sub n represents the nth term, a sub 1 represents the first term, n represents the number of the term, and d represents the common difference.
Given that the first term, a sub 1, is 6 and the common difference, d, is -4, we can substitute these values into the formula:
a sub n = 6 + (n-1)(-4)
Simplifying further:
a sub n = 6 - 4n + 4
a sub n = 10 - 4n
Therefore, the correct formula for the nth term of the arithmetic sequence is represented by option d) 10 - 4n.
So, your intuition is correct, the correct answer is d) 10 - 4n.