Answer:
C.$0.60
hope this help!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
2
Step-by-step explanation:
The second step of the solution shows division by 2 on the left. Consequently, it must also show division by 2 on the right.
2 goes in the green box
_____

Answer:
Sum of the sequence (Sn) = 33,859
Step-by-step explanation:
Given:
Sequence = 685+678+671+664+...+6
Find:
Sum of the sequence (Sn)
Computation:
a = 685
d = 678 - 985 = -7
an = 6
an = a+(n-1)d
6 = 685+(n-1)(-7)
-679 = (n-1)(-7)
97 = n-1
n = 98
So,
Sum of the sequence (Sn) = (n/2)[a+an]
Sum of the sequence (Sn) = (98/2)[685+6]
Sum of the sequence (Sn) = (49)(691)
Sum of the sequence (Sn) = 33,859
A plausible guess might be that the sequence is formed by a degree-4* polynomial,

From the given known values of the sequence, we have

Solving the system yields coefficients

so that the n-th term in the sequence might be

Then the next few terms in the sequence could very well be

It would be much easier to confirm this had the given sequence provided just one more term...
* Why degree-4? This rests on the assumption that the higher-order forward differences of
eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of
by
. Then
• 1st-order differences:

• 2nd-order differences:

• 3rd-order differences:

• 4th-order differences:

From here I made the assumption that
is the constant sequence {15, 15, 15, …}. This implies
forms an arithmetic/linear sequence, which implies
forms a quadratic sequence, and so on up
forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.