Solution/Answer |
Adding the two given equations together gives
.
Now, let the common difference be . Notice that , so we merely need to find to get the answer. The formula for an arithmetic sum is
,
where is the first term, is the number of terms, and is the common difference. Now we use this formula to find a closed form for the first given equation and the sum of the given equations. For the first equation, we have . Therefore, we have
,
or
. *(1)
For the sum of the equations (shown at the beginning of the solution) we have , so
or
*(2)
Now we have a system of equations in terms of and .
Subtracting (1) from (2) eliminates , yielding , and .
Answer: |