# Whats the missing term in the sequence 26. 16, __, 4?

##### 1 Answer

#### Explanation:

If the last term was supposed to be

If the last term is actually

Actually I favour the idea that it's the sum of the arithmetic sequence:

#-1# ,#-2# ,#-3# ,#-4#

and the geometric sequence:

#27# ,#18# ,#12# ,#8#

which would make the third term

I found this by looking at the approximate ratios between the terms, combined with some trial and error, but with hindsight I could have looked at it this way:

If

If

Since the preceding term lies between these two values, the missing term lies somewhere between

Write out the sequence:

#26, 16, 9, 4#

Write out the sequence of differences:

#-10, -7, -5#

Write out the sequence of differences of those differences:

#3,2#

Having taken differences twice we have eliminated any linear relationship - that is the constituent arithmetic sequence and are left with two terms whose ratio is that of the geometric sequence.

Since we're wanting to work with integer values, choose the first term of our geometric sequence as

#27,18,12,8#

Then subtract this from the original sequence to get:

#-1, -2, -3, -4#

Note that there are not enough constraints to determine a unique arithmetic and geometric sequence that can be added to give a sequence with first, second and fourth terms as given.

For example, if the arithmetic sequence is constant, then:

#a_n = ar^(n-1)+c#

with

and the third term is