Question

33,30,27,24,21, what’s the next number

Answer 1

18

Explanation:

It's an arithmetic sequence:

`a_1=33\\\\a_2=33-3=30\\\\a_3=30-3=27\\\\a_4=27-3=24\\\\a_5=24-3=21\\\\\text{next number}\ a_6=21-3=18`

If you need calculate any term of this sequence, then you must define an explicit formula of this sequence.

The explicit formula of an arithmetic sequence:

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

d - common difference

We have

`d=-3,\ a_1=33`

Substitute:

`a_n=33+(n-1)(-3)` use the distributive property

`a_n=33+(n)(-3)+(-1)(-3)\\\\a_n=33-3n+3\\\\a_n=36-3n`

Therefore, the next number is 6th number. Substitute n = 6:

`a_6=36-3(6)=36-18=18`

Answer 2

18

Explanation:

Do you see a pattern? Each time it decreased by 3. 33-3=30, 30-3=27, the pattern goes on, just do the same with the last shown number. 21-3=18