Sequences and Series

Hong Kong

Stage 4 - Stage 5

Consider the recurrence relation $U_{n+1}=0.5U_n+2$`U``n`+1=0.5`U``n`+2 and $U_0=20$`U`0=20.

a

Find $U_1$`U`1.

b

Find $U_2$`U`2.

c

Find $U_3$`U`3.

d

Complete the table of values.

$n$n |
$0$0 | $1$1 | $2$2 | $3$3 |
---|---|---|---|---|

$U_n$Un |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

e

Graph the relation.

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Easy

2min

Consider the recurrence relation $U_{n+1}=2U_n+100$`U``n`+1=2`U``n`+100 and $U_0=-50$`U`0=−50.

Easy

2min

Consider the recurrence relation $U_{n+1}=-2U_n-4$`U``n`+1=−2`U``n`−4 and $U_0=2$`U`0=2.

Easy

2min

Consider the recurrence relation $u_{n+1}=2u_n+2$`u``n`+1=2`u``n`+2, $u_0=2$`u`0=2.

Easy

3min

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