First we need to find what kind of sequence we have. To do that we are going to test if the sequence as a difference
, in which case it will be an arithmetic sequence, or a ratio
, in which case it will be geometric sequence.
The formula to find
is
where
is the current term in the sequence
is the previous term in the sequence
The formula to find
is
where
is the current term in the sequence
is the previous term in the sequence
- For
and
- For
and
:
Since
is equal in both procedures whereas
is not, we can conclude that our sequence is an arithmetic sequence.
Now we are going to use the explicit formula of an arithmetic sequence
where
is the nth term
is the first term
is the position of the term in the sequence
is the difference
We know that
and
, so lets replace those values in our formula:
We can conclude that the correct answer is <span>
D) an = 3n - 5</span>
64 cookies......12 broke......64 - 12 = 52 were perfect
24 more were baked.....all of them were perfect
total perfect cookies : 52 + 24 = 76 <==
20% increase in the amount of people
Oleg, Sasha, and Dima shared 600 toys. Sasha had twice as many toys as Oleg. Dima had 40 more toys than Oleg.
Let the number of toys Oleg has = x
Let the number of toys Sasha has = y
Let the number of toys Dima has = z
Sasha had twice as many toys as Oleg
So y = 2*x= 2x
Dima had 40 more toys than Oleg.
z = x + 40
Oleg, Sasha, and Dima shared 600 toys
x + y + z= 600
We know y=2x and z=x+40
Replace it for y and z
Subtract 40 on both sides
Divide by 4 on both sides
Oleg had 140 toys