Answer:
(0.84, 0.88)
Step-by-step explanation:
if you round 0.875 you get 0.88
Answer:
B
Step-by-step explanation:
You can see how the difference between two consecutive terms is constantly increasing:
![a_1 = 4](https://tex.z-dn.net/?f=a_1%20%3D%204)
![a_2 = 7 = 4+3](https://tex.z-dn.net/?f=a_2%20%3D%207%20%3D%204%2B3)
![a_3 = 12 = 7+5](https://tex.z-dn.net/?f=a_3%20%3D%2012%20%3D%207%2B5)
![a_4 = 19 = 12+7](https://tex.z-dn.net/?f=a_4%20%3D%2019%20%3D%2012%2B7)
So, for the next terms we'll have to add +9, +11, +13 and so on.
Also, note that
is obtained by adding the 2nd odd number to
,
is obtained by adding the 3rd odd number to
, and so on.
So, the recursive formula is
![a_n = a_{n-1}+(2n-1),\quad a_1=1](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn-1%7D%2B%282n-1%29%2C%5Cquad%20a_1%3D1)
For the explicit formula, recall that the sum of the first n odd numbers is n squared. Taking into account the fact that we're not starting from 1, we have
![a_n = n^2+3](https://tex.z-dn.net/?f=a_n%20%3D%20n%5E2%2B3)
=
(
−
2
y
)
(
2
)
+
6
y
−
1
+
−
1
(
(
−
4
y
)
(
2
)
−
3
y
+
9
)
=
(
−
2
y
)
(
2
)
+
6
y
+
−
1
+
−
1
(
(
−
4
y
)
(
2
)
)
+
−
1
(
−
3
y
)
+
(
−
1
)
(
9
)
=
(
−
2
y
)
(
2
)
+
6
y
+
−
1
+
8
y
+
3
y
+
−
9
=
−
4
y
+
6
y
+
−
1
+
8
y
+
3
y
+
−
9
Combine Like Terms:
=
−
4
y
+
6
y
+
−
1
+
8
y
+
3
y
+
−
9
=
(
−
4
y
+
6
y
+
8
y
+
3
y
)
+
(
−
1
+
−
9
)
=
13
y
+
−
10