Sequence: find number of multiples of 6 between 28 and 280

[hockeychick4018]

Find the number of multiples of 6 between 28 and 280. I know that it's a geometric sequence, but I don't know how to go about solving it at all. Please show work and explain when answering.

 

[mmm4444bot]

Sequences ...



Hi HockeyChick:

Please consider WHY you think of multiples as a geometric sequence instead of an arithmetic sequence.

6, 12, 18, 24, 30, ...

Are the multiples of six above generated by repeatedly ADDING a constant to an initial value, OR are they generated by repeatedly MULTIPLYING an initial value by some constant?

ARITHMETIC SEQUENCE: a + (n - 1) * r , for n = 1, 2, 3, ...

a
a + r
a + r + r
a + r + r + r
a + r + r + r + r
a + r + r + r + r + r ...

GEOMETRIC SEQUENCE: a * r^(n - 1) , for n = 1, 2, 3, ...

a
a * r
a * r * r
a * r * r * r
a * r * r * r * r
a * r * r * r * r * r ...

After you figure out which TYPE of sequence to use, write a formula for n = 1, 2, 3, ... that generates multiples of six.

Use this formula to determine the value of n required to generate the first multiple of six that you seek.

Use this formula to determine the value of n required to generate the last multiple of six that you seek.

Use these "beginning and ending" values of n that you just discovered to answer the exercise.

If you need more help, then please post your work and let us know why you're stuck.

Cheers,

~ Mark