What is the closed linear form for this sequence given a1 = -15 and an + 1 = an - 8?
A) an = 7 - 8n
B) an = -7 + 8n
C) an = -7 - 8n
D) an = -15 - 8n
my best answer is C
I will interpret that as:
a(1) = -15
a(n+1) = a(n) - 8
so each successive term decreases by 8
y = -8x + b
when x=1, y=-15
-15 = -8+b
b = -7
y = -8x - 7
or
in your variables
a(n) = -8n - 7
"your best answer" was C, correct
There is no "best answer", the others are wrong.
check your first post.
a(n+1) = a(n) - 8
a = -15
arithmetic sequence
see
http://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
a = -15
a(n) = -15 -8(n-1)= -15+8 -8n
= -7 -8n
I agree C
To find the closed linear form for the given sequence, we need to find the pattern in the sequence and represent it algebraically.
In the given sequence, we are told that a1 = -15 and an + 1 = an - 8. This means that each term is obtained by subtracting 8 from the previous term.
To find the closed linear form, we can start by listing the terms of the sequence and finding the pattern:
a1 = -15
a2 = a1 - 8 = -15 - 8 = -23
a3 = a2 - 8 = -23 - 8 = -31
a4 = a3 - 8 = -31 - 8 = -39
...
By observing the pattern, we can see that each term is obtained by subtracting 8 from the previous term.
Now, let's find a general formula for the nth term, an:
an = a1 - (n-1) * d
where a1 is the first term (-15 in this case), n is the term number, and d is the common difference (-8 in this case).
Plugging in the values, we have:
an = -15 - (n-1) * (-8)
an = -15 + 8(n-1)
an = -15 + 8n - 8
an = -23 + 8n
Therefore, the closed linear form for the given sequence is:
an = -23 + 8n
Comparing this with the given options, we find that the correct answer is B) an = -7 + 8n.
So, the correct answer is B) an = -7 + 8n.