Question

How many multiples of 4 are between 10 and 250?

Factors and multiples
ANSWERED
asked 2021-08-01
How many multiples of 4 are between 10 and 250?

Answers (1)

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.
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