If 5 times the 5th term is equal to the 6 times the 6th term of an arithmetic sequence then its 11th term is.......
I have now answered 6 of your questions without any effort on your part showing me that you have attempted these.
What do you think about this one?
Why not just follow the rules of the sequence as you stated them?
or check the related questions, where it has been solved.
n 6
To find the 11th term of an arithmetic sequence when the relationship between the terms is given, we first need to determine the common difference.
Let's assume the first term of the arithmetic sequence is represented as 'a' and the common difference as 'd'. Since the relationship states that "5 times the 5th term is equal to 6 times the 6th term," we can write the equation as:
5(a + 4d) = 6(a + 5d)
Simplifying the equation, we get:
5a + 20d = 6a + 30d
Rearranging the equation, we get:
-a = 10d
This equation implies that the common difference 'd' is equal to -a/10.
Now, to find the 11th term, we can use the formula provided for the nth term of an arithmetic sequence:
An = a + (n-1)d
Substituting the values into the formula, we have:
A11 = a + (11-1)(-a/10)
Simplifying further:
A11 = a - a/10
A11 = (10a - a)/10
A11 = 9a/10
Therefore, the 11th term of the arithmetic sequence is 9/10 times the first term, or 9a/10.