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# Translating Between Forms of Arithmetic Sequences (Grade 9)

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## Translating Between Forms of Arithmetic Sequences

1.
Given the explicit form of the arithmetic sequence $a_n = -2 + 7n$, which of the following is the recursive formula for the same sequence?
1. $a_1 = 5; \ \ a_n = a_{n-1} + 7, \ n>1$
2. $a_1 = 5; \ \ a_n = a_{n-1} - 2, \ n>1$
3. $a_1 = -2; \ \ a_n = a_{n-1} +7, \ n>1$
4. $a_1 = -2; \ \ a_n = a_{n-1} - 2, n>1$
2.
What is the recursive form of the sequence $a_n = 16-20n ?$
1. $a_1 = -20; \ \ a_n = a_{n-1} + 16, \ n>1$
2. $a_1 = 16; \ \ a_n = a_{n-1} - 20, \ n>1$
3. $a_1 = -4; \ \ a_n = a_{n-1} + 16, \ n>1$
4. $a_1 = -4; \ \ a_n = a_{n-1} - 20, \ n>1$
3.
For the sequence defined by the explicit formula $a_n = 7 + 3n$, what is the the recursive formula for this sequence?
1. $a_1 = 7; \ \ a_n = a_{n-1} + 3, \ n>1$
2. $a_1 = 10; \ \ a_n = a_{n-1} + 3, \ n>1$
3. $a_1 = 3; \ \ a_n = a_{n-1} + 7, \ n>1$
4. $a_1 = 1; \ \ a_n = a_{n-1} + 7, \ n>1$
4.
What is the recursive form of the sequence given by $a_n = 33 - 4n ?$
1. $a_1 = 33; \ \ a_n = a_{n-1} - 4, \ n>1$
2. $a_1 = -4; \ \ a_n = a_{n-1} +1, \ n>1$
3. $a_1 = 29; \ \ a_n = a_{n-1} - 4, \ n>1$
4. $a_1 = 33; \ \ a_n = a_{n-1} - 4n, \ n>1$
5.
For the sequence defined by $a_n = 2n$, how could the same sequence be written recursively? There may be more than one answer.
1. $a_1 = 2; \ \ a_n = a_{n-1} + 2, \ n>1$
2. $a_1 = 0; \ \ a_n = a_{n-1} + 2, \ n>1$
3. $a_1 = 0, a_2 = 2; \ \ a_n = a_{n-2} + 2, \ n>2$
4. $a_1 = 2, a_2 = 4; \ \ a_n = a_{n-2} + 4, \ n>2$
6.
For the sequence defined by $a_1 = 3; \ \ a_n = a_{n-1} + 5, \ n>1$, what is its explicit form?
1. $a_n = 3 - 5n$
2. $a_n = -2 + 5n$
3. $a_n = 5 - 3n$
4. $a_n = 1 - 2n$
7.
What is the explicit form of the sequence defined by $a_1 = 0; \ \ a_n = a_{n-1} + 3, \ n>1 ?$
1. $a_n = 3 + 3n$
2. $a_n = 3n$
3. $a_n = -3 + n$
4. $a_n = -3 + 3n$
8.
Given the arithmetic sequence defined by $a_1 = -10; \ \ a_n = a_{n-1} + 10, \ n>1$, what is the explicit form of this sequence?
1. $a_n = 10n$
2. $a_n = -10 + 10n$
3. $a_n = 10 - 10n$
4. $a_n = -20 + 10n$
9.
Find the explicit formula of the sequence defined by $a_1 = 85; \ \ a_n = a_{n-1} - 15, \ n>1$.
1. $a_n = 85 - 15n$
2. $a_n = -15 + 100n$
3. $a_n = 100 - 15n$
4. $a_n = 85 - 100n$
10.
For the sequence defined by $a_1 = 4; \ \ a_n = a_{n-1} - 4, n>1$, which of the following describes the same sequence? There may be more than one correct answer.
1. $a_n = 8-4n$
2. $a_n = 4 - 4(n-1)$
3. $a_n = 4 - 4n$
4. $a_n = -4 - 4(n-3)$
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