Sequences and Series

Hong Kong

Stage 4 - Stage 5

A cake is taken out of a $156^\circ$156°C oven and left to cool in a room with a constant temperature of $26^\circ$26°C.

As soon as it is taken out, the temperature of the cake drops by $2.5^\circ$2.5°C each minute.

a

What is the temperature of the cake after $8$8 minutes?

b

Write a recurrence relation that gives the temperature $T_n$`T``n` of the cake after $n$`n` minutes in terms of $T_{n-1}$`T``n`−1.

c

By how many degrees has the temperature of the cake dropped after half an hour?

d

Find the number of minutes it will take for the cake to reach room temperature.

Easy

5min

For a photo, the staff at a company have been arranged such that there are $9$9 people in the front row and each row has $2$2 more people than in the row in front of it.

Easy

4min

A basketball is dropped onto the ground from a height of $15$15 feet.

On each bounce, the ball reaches a maximum height of $55%$55% of its previous maximum height.

Easy

6min

Farhan has saved up $\$2540$$2540 to spend during his holiday to Lebanon. He plans to spend $\$310$$310 each week while he is there.

Let $t_n$`t``n` be the amount of savings Farhan has left at the beginning of week $n$`n`.

Easy

3min

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