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Math Problems
Algebra 1
Convert a recursive formula to an explicit formula
The indicated value by writing & solving a system of linear equations using
D
=
R
∗
T
D=R*T
D
=
R
∗
T
.
\newline
Chase and Charlie decided to take a
10
10
10
mile canoe trip down the Crow Wing River. To get to their destination it took them
2
2
2
hours, but because of the current, it took them
31
3
\frac{31}{3}
3
31
hours to get home. How fast were they paddling and what was the rate of the current?
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Find the sum of the first
35
35
35
terms of the following series, to the nearest integer.
\newline
11
,
17
,
23
,
…
11,17,23, \ldots
11
,
17
,
23
,
…
\newline
Answer:
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
4
4
4
, and the seventh term,
a
7
a_{7}
a
7
, is equal to
40
40
40
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
5
d=5
d
=
5
\newline
d
=
6
d=6
d
=
6
\newline
d
=
7
d=7
d
=
7
\newline
d
=
8
d=8
d
=
8
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
8
8
8
, and the fifth term,
a
5
a_{5}
a
5
, is equal to
20
20
20
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
2
d=2
d
=
2
\newline
d
=
3
d=3
d
=
3
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
9
9
9
, and the fourth term,
a
4
a_{4}
a
4
, is equal to
39
39
39
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
9
d=9
d
=
9
\newline
d
=
10
d=10
d
=
10
\newline
d
=
11
d=11
d
=
11
\newline
d
=
12
d=12
d
=
12
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
5
5
5
, and the sixth term,
a
6
a_{6}
a
6
, is equal to
15
15
15
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
2
d=2
d
=
2
\newline
d
=
3
d=3
d
=
3
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
5
5
5
, and the sixth term,
a
6
a_{6}
a
6
, is equal to
30
30
30
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
\newline
d
=
6
d=6
d
=
6
\newline
d
=
7
d=7
d
=
7
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
1
1
1
, and the fourth term,
a
4
a_{4}
a
4
, is equal to
27
27
27
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
1
r=1
r
=
1
\newline
r
=
2
r=2
r
=
2
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
9
9
9
, and the sixth term,
a
6
a_{6}
a
6
, is equal to
24
24
24
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
2
d=2
d
=
2
\newline
d
=
3
d=3
d
=
3
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
5
5
5
, and the seventh term,
a
7
a_{7}
a
7
, is equal to
29
29
29
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
\newline
d
=
6
d=6
d
=
6
\newline
d
=
7
d=7
d
=
7
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Use the initial term and the recursive formula to find an explicit formula for the sequence
a
n
a_n
a
n
. Write your answer in simplest form.
\newline
a
1
=
1
a_1 = 1
a
1
=
1
\newline
a
n
=
a
n
−
1
+
14
a_n = a_{n - 1} + 14
a
n
=
a
n
−
1
+
14
\newline
a
n
=
a_n =
a
n
=
______
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