NZ Level 7 (NZC) Level 2 (NCEA) Recurrence relationships for GP's

## Interactive practice questions

Consider the first-order recurrence relationship defined by $T_n=2T_{n-1},T_1=2$Tn=2Tn1,T1=2.

a

Determine the next three terms of the sequence from $T_2$T2 to $T_4$T4.

Write all three terms on the same line, separated by commas.

b

Plot the first four terms on the graph below.

c

Is the sequence generated from this definition arithmetic or geometric?

Arithmetic

A

Geometric

B

Neither

C

Arithmetic

A

Geometric

B

Neither

C
Easy
Approx 2 minutes

Consider the sequence plot drawn below.

Consider the sequence $9000,1800,360,72,\dots$9000,1800,360,72,

Write a recursive rule for $T_n$Tn in terms of $T_{n-1}$Tn1 and an initial condition for $T_1$T1.

Write both parts on the same line separated by a comma.

Consider the sequence $40$40, $20$20, $10$10, $5$5, $\text{. . .}$. . .

### Outcomes

#### M7-3

Use arithmetic and geometric sequences and series

#### 91258

Apply sequences and series in solving problems