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# Sequences and Series Questions - All Grades

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What is the explicit function of the geometric sequence 3, 4.5, 6.75, ...?
1. $f(n)=1.5f(n-1)$ where $f(1)=3$
2. $f(n)=3*1.5^(n-1)$
3. $f(n)=1.5*3^(n-1)$
4. $f(n)=3f(n-1)$ where $f(1)=1.5$
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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. $a_1 = -2; \ \ a_n = a_{n-1} - 2, n>1$
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4
Find the sum of the finite geometric series.
$1+4+16+64 +...+4^9$
1. $516$
2. $2","073.3$
3. $25","347$
4. $349","525$
5. None of these are correct
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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. $a_n = 1 - 2n$
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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. $a_n = -20 + 10n$
Each number in a sequence.
1. Sequence
2. Term
3. Arithmetic Sequence
Given the sequence $1,4,16,64,256,...$, which of the following correctly defines this sequence in a recursive form? Assume that $n in NN$.
1. $t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1$
2. $t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1$
3. $t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1$
4. $t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1$
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
What are the next 2 numbers in the sequence $1, 5, 9...$?
1. $45,225$
2. $14,18$
3. $13,17$
4. $32,128$
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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. $a_1 = 2, a_2 = 4; \ \ a_n = a_{n-2} + 4, \ n>2$
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
What is the $n^(th)$ term of the arithmetic progression, $-3, -8, -13, ...$?
1. $2+5n$
2. $8+5n$
3. $2-5n$
4. $8-5n$
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
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