Write the explicit equation for the sequence. 3, 15, 75, 375,...

f ( n ) = 3 ( 5 ) ( n − 1 ) f\left(n\right)=3\left(5\right)^{\left(n-1\right)} f ( n ) = 3 ( 5 ) ( n − 1 )

f ( n ) = 3 ( 5 ) n f\left(n\right)=3\left(5\right)^n f ( n ) = 3 ( 5 ) n

f ( n ) = 5 ( 3 ) n f\left(n\right)=5\left(3\right)^n f ( n ) = 5 ( 3 ) n

f ( n ) = 5 ( 3 ) ( n − 1 ) f\left(n\right)=5\left(3\right)^{\left(n-1\right)} f ( n ) = 5 ( 3 ) ( n − 1 )

Write the recursive equation for the sequence. 3, 15, 75, 375,...

f ( n ) = f ( n − 1 ) ⋅ 5 , f ( 1 ) = 3 f\left(n\right)=f\left(n-1\right)\cdot5,\ f\left(1\right)=3 f ( n ) = f ( n − 1 ) ⋅ 5 , f ( 1 ) = 3

f ( n ) = f ( n − 1 ) ⋅ 3 , f ( 1 ) = 5 f\left(n\right)=f\left(n-1\right)\cdot3,\ f\left(1\right)=5 f ( n ) = f ( n − 1 ) ⋅ 3 , f ( 1 ) = 5

Write the explicit equation for the sequence. 3, -9, -21, -33,...

f ( n ) = 3 − 12 ( n − 1 ) f\left(n\right)=3-12\left(n-1\right) f ( n ) = 3 − 1 2 ( n − 1 )

f ( n ) = 3 + 12 n f\left(n\right)=3+12n f ( n ) = 3 + 1 2 n

f ( n ) = 3 − 12 n f\left(n\right)=3-12n f ( n ) = 3 − 1 2 n

f ( n ) = 3 + 12 ( n − 1 ) f\left(n\right)=3+12\left(n-1\right) f ( n ) = 3 + 1 2 ( n − 1 )

Write the recursive equation for the sequence. 3, -9, -21, -33,...

f ( n ) = f ( n − 1 ) − 12 , f ( 1 ) = 3 f\left(n\right)=f\left(n-1\right)-12,\ f\left(1\right)=3 f ( n ) = f ( n − 1 ) − 1 2 , f ( 1 ) = 3

f ( n ) = f ( n − 1 ) + 12 , f ( 1 ) = 3 f\left(n\right)=f\left(n-1\right)+12,\ f\left(1\right)=3 f ( n ) = f ( n − 1 ) + 1 2 , f ( 1 ) = 3

Using the graph, what is the recursive equation?

f ( n ) = f ( n − 1 ) − 2 , f ( 1 ) = 9 f\left(n\right)=f\left(n-1\right)-2,\ f\left(1\right)=9 f ( n ) = f ( n − 1 ) − 2 , f ( 1 ) = 9

f ( n ) = f ( n − 1 ) + 2 , f ( 1 ) = 9 f\left(n\right)=f\left(n-1\right)+2,\ f\left(1\right)=9 f ( n ) = f ( n − 1 ) + 2 , f ( 1 ) = 9

Using the graph, what is the explicit equation?

f ( n ) = 9 − 2 ( n − 1 ) f\left(n\right)=9-2\left(n-1\right) f ( n ) = 9 − 2 ( n − 1 )

f ( n ) = 9 − 2 n f\left(n\right)=9-2n f ( n ) = 9 − 2 n

f ( n ) = 9 + 2 ( n − 1 ) f\left(n\right)=9+2\left(n-1\right) f ( n ) = 9 + 2 ( n − 1 )

f ( n ) = 9 + 2 n f\left(n\right)=9+2n f ( n ) = 9 + 2 n

Using the graph, what is the recursive equation?

f ( n ) = f ( n − 1 ) ⋅ 2 , f ( 1 ) = 0.5 f\left(n\right)=f\left(n-1\right)\cdot2,\ f\left(1\right)=0.5 f ( n ) = f ( n − 1 ) ⋅ 2 , f ( 1 ) = 0 . 5

f ( n ) = f ( n − 1 ) + 2 , f ( 1 ) = 0.5 f\left(n\right)=f\left(n-1\right)+2,\ f\left(1\right)=0.5 f ( n ) = f ( n − 1 ) + 2 , f ( 1 ) = 0 . 5

Using the graph, what is the explicit equation?

f ( n ) = 0.5 ( 2 ) ( n − 1 ) f\left(n\right)=0.5\left(2\right)^{\left(n-1\right)} f ( n ) = 0 . 5 ( 2 ) ( n − 1 )

f ( n ) = 2 ( 0.5 ) ( n − 1 ) f\left(n\right)=2\left(0.5\right)^{\left(n-1\right)} f ( n ) = 2 ( 0 . 5 ) ( n − 1 )

f ( n ) = 0.5 + 2 ( n − 1 ) f\left(n\right)=0.5+2\left(n-1\right) f ( n ) = 0 . 5 + 2 ( n − 1 )

f ( n ) = 2 + 0.5 ( n − 1 ) f\left(n\right)=2+0.5\left(n-1\right) f ( n ) = 2 + 0 . 5 ( n − 1 )

The first term of a sequence is 300. The sequence increases by 9% each term. Create an explicit equation for this sequence.

f ( n ) = 300 ( 1.09 ) ( n − 1 ) f\left(n\right)=300\left(1.09\right)^{\left(n-1\right)} f ( n ) = 3 0 0 ( 1 . 0 9 ) ( n − 1 )

f ( n ) = 300 ( . 09 ) ( n − 1 ) f\left(n\right)=300\left(.09\right)^{\left(n-1\right)} f ( n ) = 3 0 0 ( . 0 9 ) ( n − 1 )

f ( n ) = 300 ( . 9 ) ( n − 1 ) f\left(n\right)=300\left(.9\right)^{\left(n-1\right)} f ( n ) = 3 0 0 ( . 9 ) ( n − 1 )

f ( n ) = 300 ( 1.9 ) ( n − 1 ) f\left(n\right)=300\left(1.9\right)^{\left(n-1\right)} f ( n ) = 3 0 0 ( 1 . 9 ) ( n − 1 )

The first term of a sequence is 45. The sequence decreases by 15% each term. Create an explicit equation for this sequence.

f ( n ) = 45 ( . 85 ) ( n − 1 ) f\left(n\right)=45\left(.85\right)^{\left(n-1\right)} f ( n ) = 4 5 ( . 8 5 ) ( n − 1 )

f ( n ) = 45 ( . 15 ) ( n − 1 ) f\left(n\right)=45\left(.15\right)^{\left(n-1\right)} f ( n ) = 4 5 ( . 1 5 ) ( n − 1 )

f ( n ) = 45 ( 1.15 ) ( n − 1 ) f\left(n\right)=45\left(1.15\right)^{\left(n-1\right)} f ( n ) = 4 5 ( 1 . 1 5 ) ( n − 1 )

f ( n ) = 45 ( . 95 ) ( n − 1 ) f\left(n\right)=45\left(.95\right)^{\left(n-1\right)} f ( n ) = 4 5 ( . 9 5 ) ( n − 1 )

If the recursive equation of a sequence is f ( n ) = f ( n − 1 ) ⋅ 9 , f ( 1 ) = 2 f\left(n\right)=f\left(n-1\right)\cdot9,\ f\left(1\right)=2 f ( n ) = f ( n − 1 ) ⋅ 9 , f ( 1 ) = 2 what is the explicit equation of the sequence?

f ( n ) = 2 ( 9 ) ( n − 1 ) f\left(n\right)=2\left(9\right)^{\left(n-1\right)} f ( n ) = 2 ( 9 ) ( n − 1 )

f ( n ) = 9 ( 2 ) ( n − 1 ) f\left(n\right)=9\left(2\right)^{\left(n-1\right)} f ( n ) = 9 ( 2 ) ( n − 1 )

f ( n ) = 9 + 2 ( n − 1 ) f\left(n\right)=9+2\left(n-1\right) f ( n ) = 9 + 2 ( n − 1 )

f ( n ) = 2 + 9 ( n − 1 ) f\left(n\right)=2+9\left(n-1\right) f ( n ) = 2 + 9 ( n − 1 )

If the explicit equation for a sequence is f ( n ) = 4 ( 6 ) ( n − 1 ) f\left(n\right)=4\left(6\right)^{\left(n-1\right)} f ( n ) = 4 ( 6 ) ( n − 1 ) , what would the recursive equation for the sequence be?

f ( n ) = f ( n − 1 ) ⋅ 6 , f ( 1 ) = 4 f\left(n\right)=f\left(n-1\right)\cdot6,\ f\left(1\right)=4 f ( n ) = f ( n − 1 ) ⋅ 6 , f ( 1 ) = 4

f ( n ) = f ( n − 1 ) ⋅ 4 , f ( 1 ) = 6 f\left(n\right)=f\left(n-1\right)\cdot4,\ f\left(1\right)=6 f ( n ) = f ( n − 1 ) ⋅ 4 , f ( 1 ) = 6

f ( n ) = f ( n − 1 ) ⋅ 4 , f ( 0 ) = 6 f\left(n\right)=f\left(n-1\right)\cdot4,\ f\left(0\right)=6 f ( n ) = f ( n − 1 ) ⋅ 4 , f ( 0 ) = 6

f ( n ) = f ( n − 1 ) ⋅ 6 , f ( 0 ) = 4 f\left(n\right)=f\left(n-1\right)\cdot6,\ f\left(0\right)=4 f ( n ) = f ( n − 1 ) ⋅ 6 , f ( 0 ) = 4

If the explicit equation for a sequence is f ( n ) = 2 ( 5 ) ( n − 3 ) f\left(n\right)=2\left(5\right)^{\left(n-3\right)} f ( n ) = 2 ( 5 ) ( n − 3 ) , what would the recursive equation for the sequence be?

f ( n ) = f ( n − 1 ) ⋅ 5 , f ( 3 ) = 2 f\left(n\right)=f\left(n-1\right)\cdot5,\ f\left(3\right)=2 f ( n ) = f ( n − 1 ) ⋅ 5 , f ( 3 ) = 2

f ( n ) = f ( n − 1 ) ⋅ 5 , f ( 1 ) = 2 f\left(n\right)=f\left(n-1\right)\cdot5,\ f\left(1\right)=2 f ( n ) = f ( n − 1 ) ⋅ 5 , f ( 1 ) = 2

f ( n ) = f ( n − 1 ) ⋅ 2 , f ( 1 ) = 5 f\left(n\right)=f\left(n-1\right)\cdot2,\ f\left(1\right)=5 f ( n ) = f ( n − 1 ) ⋅ 2 , f ( 1 ) = 5

f ( n ) = f ( n − 1 ) ⋅ 2 , f ( 3 ) = 5 f\left(n\right)=f\left(n-1\right)\cdot2,\ f\left(3\right)=5 f ( n ) = f ( n − 1 ) ⋅ 2 , f ( 3 ) = 5

If the recursive equation of a sequence is f ( n ) = f ( n − 1 ) − 15 , f ( 0 ) = 8 f\left(n\right)=f\left(n-1\right)-15,\ f\left(0\right)=8 f ( n ) = f ( n − 1 ) − 1 5 , f ( 0 ) = 8 what is the explicit equation of the sequence?

f ( n ) = 8 − 15 n f\left(n\right)=8-15n f ( n ) = 8 − 1 5 n

f ( n ) = 8 − 15 ( n − 1 ) f\left(n\right)=8-15\left(n-1\right) f ( n ) = 8 − 1 5 ( n − 1 )

f ( n ) = − 15 + 8 ( n − 1 ) f\left(n\right)=-15+8\left(n-1\right) f ( n ) = − 1 5 + 8 ( n − 1 )

f ( n ) = − 15 + 8 n f\left(n\right)=-15+8n f ( n ) = − 1 5 + 8 n

Sequences

Quiz

•

Mathematics

•

9th - 10th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.BF.A.2, HSF.IF.A.3, HSF.LE.A.2

+1

Standards-aligned

Nicole Ramsey

Used 11+ times

FREE Resource

23 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Is the sequence arithmetic, geometric, or neither?
4, 10, 25, 62.5,...

Arithmetic

Geometric

Neither

Tags

CCSS.HSF.BF.A.2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Is the sequence arithmetic, geometric, or neither?
2, 3, 5, 8,...

Arithmetic

Geometric

Neither

Tags

CCSS.HSF.BF.A.2

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Is the sequence arithmetic, geometric, or neither?
2, 7.5, 13, 18.5,...

Arithmetic

Geometric

Neither

Tags

CCSS.HSF.BF.A.2

4.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

What is the common difference of the arithmetic sequence?
42, 73, 104, 135,...

Tags

CCSS.HSF.BF.A.2

5.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

What is the common difference of the arithmetic sequence?
17, 5, -7, -19,...

Tags

CCSS.HSF.BF.A.2

6.

FILL IN THE BLANK QUESTION

1 min • 1 pt

What is the common ratio of the geometric sequence?
8, 28, 98, 343,...

Tags

CCSS.HSF.BF.A.2

7.

FILL IN THE BLANK QUESTION

1 min • 1 pt

What is the common ratio of the geometric sequence?
15, 12, 9.6, 7.68,...

Tags

CCSS.HSF.BF.A.2

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Sequences

23 questions

Is the sequence arithmetic, geometric, or neither?4, 10, 25, 62.5,...

Is the sequence arithmetic, geometric, or neither?2, 3, 5, 8,...

Is the sequence arithmetic, geometric, or neither?2, 7.5, 13, 18.5,...

What is the common difference of the arithmetic sequence?42, 73, 104, 135,...

What is the common difference of the arithmetic sequence?17, 5, -7, -19,...

What is the common ratio of the geometric sequence?8, 28, 98, 343,...

What is the common ratio of the geometric sequence?15, 12, 9.6, 7.68,...

Write the explicit equation for the sequence.3, 15, 75, 375,...

Write the recursive equation for the sequence.3, 15, 75, 375,...

Write the explicit equation for the sequence.3, -9, -21, -33,...

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Is the sequence arithmetic, geometric, or neither?
4, 10, 25, 62.5,...

Is the sequence arithmetic, geometric, or neither?
2, 3, 5, 8,...

Is the sequence arithmetic, geometric, or neither?
2, 7.5, 13, 18.5,...

What is the common difference of the arithmetic sequence?
42, 73, 104, 135,...

What is the common difference of the arithmetic sequence?
17, 5, -7, -19,...

What is the common ratio of the geometric sequence?
8, 28, 98, 343,...

What is the common ratio of the geometric sequence?
15, 12, 9.6, 7.68,...

Write the explicit equation for the sequence.
3, 15, 75, 375,...

Write the recursive equation for the sequence.
3, 15, 75, 375,...

Write the explicit equation for the sequence.
3, -9, -21, -33,...