In triangle ABC , M and N are midpoints of sides. If MN = 2x + 5 and BC = x2 − 2, find the possible lengths for MN.
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1. Let 
be the number of seats in the 
-th row. The number seats in the -th row relative to the number of seats in the 
-th row is given by the recursive rule
Since
, we have
So the explicit rule for the sequence is
In the 15th row, the number of seats is
2. Let
be the amount of profit in the -th year. If the profits increase by 6% each year, we would have
with
.
The second part of the question is somewhat vague - are we supposed to find the profits in the 20th year alone? the total profits in the first 20 years? I'll assume the first case, in which we would have a profit of
3. Now let denote the number of pushups done in the -th week. Since 
, 
, and 
, it looks like we can expect the number of pushups to quadruple per week. So,
starting with
.
We can apply the same reason as in (2) to find the explicit rule for the sequence, which you'd find to be
Since
So the explicit rule for the sequence
In the 15th row, the number of seats is
2. Let
with
The second part of the question is somewhat vague - are we supposed to find the profits in the 20th year alone? the total profits in the first 20 years? I'll assume the first case, in which we would have a profit of
3. Now let
starting with
We can apply the same reason as in (2) to find the explicit rule for the sequence, which you'd find to be