by Quelloquialism » Wed Jul 11, 2007 1:57 pm
My solution:
Define the first term of the first sequence to be [unparseable or potentially dangerous latex formula], the common difference of the first sequence to be [unparseable or potentially dangerous latex formula], the first term of the second sequence to be [unparseable or potentially dangerous latex formula], and the common difference of the second sequence to be [unparseable or potentially dangerous latex formula].
Equation 1: [unparseable or potentially dangerous latex formula]
Equation 2: [unparseable or potentially dangerous latex formula]
Equation 3: [unparseable or potentially dangerous latex formula]
Multiply out Equation 3.
Equation 4: [unparseable or potentially dangerous latex formula]
Multiply out Equation 2.
[unparseable or potentially dangerous latex formula]
Multiply the result by 2.
Equation 5: [unparseable or potentially dangerous latex formula]
Subtract Equation 4 from Equation 5.
[unparseable or potentially dangerous latex formula]
Substitute in Equation 1.
[unparseable or potentially dangerous latex formula]
Combine the constant values.
[unparseable or potentially dangerous latex formula]
Divide by -2.
Equation 6: [unparseable or potentially dangerous latex formula]
Now, take Equation 4 again.
[unparseable or potentially dangerous latex formula]
Substitute in Equation 1 and Equation 6.
[unparseable or potentially dangerous latex formula]
Combine the constant values.
Equation 7: [unparseable or potentially dangerous latex formula]
The eighth term should be...
[unparseable or potentially dangerous latex formula]
Multiply this out.
[unparseable or potentially dangerous latex formula]
Factor out the 7 in the middle two terms.
[unparseable or potentially dangerous latex formula]
Substitute in Equation 1, Equation 6, and Equation 7.
[unparseable or potentially dangerous latex formula]
Essentially the same solution.