Two arithmetic sequences have the same first term. The $5^{\mathrm{th}}$ term of the first sequence and the $4^{\mathrm{th}}$ term of the second are both equal to $16$. The $9^{\mathrm{th}}$ term of the first sequence and the $7^{\mathrm{th}}$ term of the second are both equal to $28$. Find the first term and common difference of each sequence.

Sometimes a real-life problem can be modelled using an arithmetic or geometric sequence. Consider the following scenarios and decide if it could be described using an arithmetic or a geometric sequence, and explain why. Also, write down what the terms of the sequence would represent.

You are saving up for a summer trip. Your parents give you $\$10$ to get you started, and then you save half your pocket money each month. (Your pocket money is the same amount every month.)

Sometimes a real-life problem can be modelled using an arithmetic or geometric sequence. Consider the following scenarios and decide if it could be described using an arithmetic or a geometric sequence, and explain why. Also, write down what the terms of the sequence would represent.

The population of the Earth is increasing by $1.13\%$ per year. This means that next year it will have increased by a factor of $1.0113$.

Sometimes a real-life problem can be modelled using an arithmetic or geometric sequence. Consider the following scenarios and decide if it could be described using an arithmetic or a geometric sequence, and explain why. Also, write down what the terms of the sequence would represent.

Sometimes a real-life problem can be modelled using an arithmetic or geometric sequence. Consider the following scenarios and decide if it could be described using an arithmetic or a geometric sequence, and explain why. Also, write down what the terms of the sequence would represent.

The owners of a new coffee shop are trying to work out how their customer numbers will grow in the first year. They think that each month, $20$ new customers will find their business.

Sometimes a real-life problem can be modelled using an arithmetic or geometric sequence. Consider the following scenarios and decide if it could be described using an arithmetic or a geometric sequence, and explain why. Also, write down what the terms of the sequence would represent.

A population of Chloroflexi bacteria doubles in number every $27$ minutes. A researcher records the size of the population every hour after the start of the experiment.
 

Sometimes a real-life problem can be modelled using an arithmetic or geometric sequence. Consider the following scenarios and decide if it could be described using an arithmetic or a geometric sequence, and explain why. Also, write down what the terms of the sequence would represent.

Outside my house the snow is $15 \mathrm{cm}$ deep one morning. As the snow melts, the total depth of snow decreases by $15\%$ every hour.