soyboy5000
Answered

How many multiples of 3 are there between 100 and 1,000?


Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.


266

299

300

301

Verified Answer :

what? Umm for one that just confussed me Alot i am slow not that slow do you know what pdd is and hdd or i.e.p just asking to me thats like 12th or collage math work?

There are 300 multiples of 3 between 100 and 1,000. So, the third option is correct.

Important information:

  • We need to find the number of multiples of 3 between 100 and 1,000.

Arithmetic progression:

The multiples of 3 between 100 and 1,000 are 102, 105, ...., 999.

First term is 102, the common difference is 3 and the last term is 999.

The nth term of an Arithmetic progression is:

\(a_n=a_1+(n-1)d\)

Where, \(a_1\) is first term and \(d\) is the common difference.

\(999=102+(n-1)3\)

\(999=102+3n-3\)

\(999=99+3n\)

Isolate the variable.

\(999-99=3n\)

\(900=3n\)

\(\dfrac{900}{3}=n\)

\(300=n\)

Therefore, the third option is correct.

Find out more about 'Arithmetic progression' here:

https://brainly.com/question/24873057

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