How do you determine whether each sequence could be geometric, arithmetic, or neither. Use a patte to write the next three terms. 460, 46, 4.6, 0.46?

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Answer 1 · 2018-02-16T11:34:08

See below.

If a, b, c are in arithmetic sequence then:

#b-a=c-b#

This is known as the common difference

If a, b, c are in geometric sequence then:

#b/a=c/b#

This is known as the common ratio

From given sequence:

#460, 46, 4.6, 0.46#

#b-a=c-b#

#46-460=-414#

#4.6-46=-41.4#

#-414!=-41.4color(white)(88)# not an arithmetic sequence

#b/a=c/b#

#46/460=0.1#

#4.6/46=0.1color(white)(88)#This is a geometric sequence

The nth term of a geometric sequence is given by:

#ar^(n-1)#

Where #bba# is the first term, #bbr# is the common ratio and #bbn# is the #bb(nth)# term.

From example:

#bba=460#

#bbr=0.1#

We need to find the next 3 terms. i.e. 5th 6th and 7th.

So:

#5"th" = 460(0.1)^4=0.046#

#6"th" = 460(0.1)^5=0.0046#

#7"th" = 460(0.1)^6=0.00046#

We can see from the pattern, that as the sequence progresses each number is 10 times smaller than the previous number.