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
