Sequences and Series

Hong Kong

Stage 4 - Stage 5

Consider the first-order recurrence relationship defined by $T_n=2T_{n-1},T_1=2$`T``n`=2`T``n`−1,`T`1=2.

a

Determine the next three terms of the sequence from $T_2$`T`2 to $T_4$`T`4.

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

b

Plot the first four terms on the graph below.

Loading Graph...

c

Is the sequence generated from this definition arithmetic or geometric?

Arithmetic

A

Geometric

B

Neither

C

Easy

2min

Consider the sequence plot drawn below.

Easy

1min

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

Write a recursive rule for $T_n$`T``n` in terms of $T_{n-1}$`T``n`−1 and an initial condition for $T_1$`T`1.

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

Easy

1min

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

Easy

1min

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