given the arithmetic sequence 71,65,59 ... if a(n) is -43 what is the value of n
a = 71, d = -6
term(n) = a + (n-1)d
-43 = 71 + (n-1)(-6)
-43 = 71 - 6n + 6
6n = 120
n = 20
Answer
To find the value of n in the arithmetic sequence 71, 65, 59, ..., where a(n) is -43, we can use the formula for the nth term of an arithmetic sequence:
a(n) = a(1) + (n - 1)d
In this formula, a(n) represents the nth term, a(1) is the first term in the sequence, n is the position of the term you want to find, and d is the common difference between terms.
From the given sequence, we can see that the first term, a(1), is 71 and the common difference, d, is -6.
Plugging these values into the formula, we have:
-43 = 71 + (n - 1)(-6)
Now we can solve for n.
-43 = 71 - 6n + 6
-43 - 71 = -6n
-114 = -6n
n = -114 / (-6)
n = 19
Therefore, the value of n is 19.