Free Printable Recursive Equations: Unit 1 Test Review

1.

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

a)

-16, -21, -26, -31

b)

5, -11, -27, -43

c)

-16, -80, -500, -200

d)

-16, -11, -6, -1

2.

Write a recursive rule for the sequence 17, 1, -15, -31 . . .

a)

a_n = a_n-1 + 16
a₁=17

b)

a_n = a_n-1 - 17
a₁=17

c)

a_n = a_n-1 - 15
a₁=17

d)

a_n = a_n-1 - 16
a₁=17

3.

Given the first five terms, write the recursive formula.
15, 12, 9, 6, 3 ....

a)

u₁ = 15
u_n = u_n-1 + 3

b)

u₀ = 15
u_n = u_n-1 + 3

c)

u₁ = 15
u_n = u_n-1 - 3

d)

u₀ = 15
u_n = u_n-1 - 3

4.

Given the recursive formula below, find the explicit formula.

a₁= 6

a_n = a_n-1 + 5

a)

a_n= 6 + 5n

b)

a_n = 1 + 5n

c)

a_n= 11 + 5n

d)

a_n= -4 + 5n

5.

Given the recursive formula below, find the explicit formula.

a₁= 5

a_n = a_n-1 - 6

a)

a_n = 5 - 6n

b)

a_n = 11 - 6n

c)

a_n = -6 +5n

d)

a_n = -6 + 11n

6.

Which of the following recursive formulas represents the given sequence.

7, 14, 28, 56, 112, ...

a)

$a_1=7$ , $a_n=a_{\left(n-1\right)}+7$

b)

$a_1=7$ , $a_n=a_{\left(n-1\right)}\cdot7$

c)

$a_1=7$ , $a_n=a_{\left(n-1\right)}\cdot2$

d)

$a_1=7$ , $a_n=a_{\left(n-1\right)}+14$

7.

Determine the 3rd term of the sequence.
$a_1=5$

a_n=2\cdot a_{n-1}-1

a)

14

b)

13

c)

17

d)

16

8.

Given the recursive formula, find the explicit form

a_n = a_n-1 - 5

a₁ = 22

a)

a_n = 22 - 5(n-1)

b)

a_n = 22 +5 (n-1)

c)

a_n = -5 + 22n

d)

a_n = 22-5n

9.

Determine the first 3 terms of the following sequence. $t_n=3\cdot t_{n-1}$ , $t_1=-3$

a)

-3, 9, 27

b)

-3, -9, -27

c)

-3, -6, -9

d)

-3, 6,9

10.

$f\left(n\right)=\ \ 24\ \left(\frac{1}{2}\right)^{\left(n-1\right)}$ Given the explicit formula, find the recursive equation.

a)

$a_1=24$ , $a_n=\frac{1}{2}\cdot a_{n-1}$

b)

$a_1=24$ , $a_n=2\cdot a_{n-1}$

c)

$a_1=12,\ a_n=\frac{1}{2}\cdot a_{n-1}$

d)

$a_1=48,\ a_n=\frac{1}{2}\cdot a_{n-1}$

Recursive Equations: Unit 1 Test Review

Total questions: 10

Worksheet time: 50mins

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