In an arithmetic sequence, the first term is 100 and the sixth term is 85. Find the common difference. Then, find the 50th term of the sequence.
Do I use the formula an=a1+(n-1)d?
If so, what would my "n" by in the equation?
The nth term of an arithmetic progression is defined by N = a + (n-1)d where N = the nth term, a = the first term and d = the common difference.
Therefore,
85 = 100 + (6 - 1)d
-15 = 5d making d = -3
The 50th term then becomes
N(50) = 85 + (50 - 1)(-3) = ?
ah what!!!!!!!!!!!!!!!!!!!
Yes, you can use the formula an = a1 + (n-1)d to find the nth term in an arithmetic sequence, where a1 is the first term, d is the common difference, and n is the term number you want to find.
In this case, you are given the first term (a1 = 100) and the sixth term (a6 = 85). You want to find the common difference (d) and the 50th term (a50).
To find the common difference (d), you can use the formula:
a6 = a1 + (6-1)d
Plugging in the given values:
85 = 100 + 5d
Now, you can solve for d:
85 - 100 = 5d
-15 = 5d
d = -15/5
d = -3
So, the common difference is -3.
To find the 50th term (a50), you can use the same formula, but this time the term number is 50:
a50 = a1 + (50-1)d
Substituting the values:
a50 = 100 + (50-1)(-3)
Simplifying the expression:
a50 = 100 + 49(-3)
a50 = 100 - 147
a50 = -47
Therefore, the 50th term of the sequence is -47.