Question

# How many multiples of 4 are between 10 and 250?

Factors and multiples
How many multiples of 4 are between 10 and 250?

2021-08-02
Step 1
The multiples of 4 that lie between 10 and 250 are 12,16,20,....,248
Step 2
$$\displaystyle{a}_{{{1}}}={a}={12}$$
$$\displaystyle{a}_{{{2}}}={16}$$
$$\displaystyle{d}={a}_{{{2}}}-{a}_{{{1}}}$$
$$\displaystyle={16}-{12}$$
$$\displaystyle={4}$$
$$\displaystyle{a}_{{{n}}}={a}+{\left({n}-{1}\right)}{d}$$
$$\displaystyle{248}={12}+{\left({n}-{1}\right)}{4}$$
$$\displaystyle{248}-{12}={4}{n}-{4}$$
$$\displaystyle{236}={4}{n}-{4}$$
$$\displaystyle{4}{n}={240}$$
$$\displaystyle{n}={\frac{{{240}}}{{{4}}}}$$
$$\displaystyle{n}={60}$$
The number of multiples of 4 that lie between 10 and 250 is 60.