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\(\pi\)
e
\(\frac{a}{b}\)
!
←
→
(
)
\(\sqrt{\,}\)
\(a^{b}\)
7
8
9
\(\div\)
log
ln
4
5
6
\(\times\)
cos
cos⁻¹
1
2
3
-
sin
sin⁻¹
0
.
=
+
tan
tan⁻¹
Consider the sequence \( (u_0=125,\ u_1=115,\ u_2=105,\ u_3=95,\,\ldots) \).
\(u_1-u_0 =\)
7
8
9
+
4
5
6
-
1
2
3
*
C
0
.
÷
\(u_2-u_1 =\)
7
8
9
+
4
5
6
-
1
2
3
*
C
0
.
÷
\(u_3-u_2 =\)
7
8
9
+
4
5
6
-
1
2
3
*
C
0
.
÷
Show that the sequence is arithmetic.
The difference between consecutive terms is constant.
The ratio of consecutive terms is constant.
The terms alternate in sign.
What is its recursive rule?
\(u_{n+1}=\)
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(i\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
\(C\)
7
8
9
←
→
\(\sin{\,}\)
4
5
6
(
)
\(\cos{\,}\)
1
2
3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
.
+
-
=
What is its explicit rule?
\(u_{n}=\)
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(i\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
\(C\)
7
8
9
←
→
\(\sin{\,}\)
4
5
6
(
)
\(\cos{\,}\)
1
2
3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
.
+
-
=
Find the 1000th term of the sequence.
\(u_{1000}=\)
7
8
9
+
4
5
6
-
1
2
3
*
C
0
.
÷
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