Expert Answers
pohnpei397 eNotes educator| Certified Educator

This is clearly an arithmetic progression.  That means that it is a series of numbers in which the difference betwee each pair of consecutive numbers is exactly the same.  In this case, the difference between the two pairs of consecutive numbers is 11.  There is a difference of 11 between 75 and 64 and a difference of 11 between 64 and 53.

Therefore, to find the next number in the progression, we only need to subtract 11 from 53.  That is, of course, 42.

So the next number in this sequence is 42.

hala718 eNotes educator| Certified Educator

75, 64, 53, ....

We notice that the numbers above are terms of an arthimatical progression where r= -11 and first term a1= 75

a1= 75

a2= 75 + -11 = 64

a3= 75+ -11*2 = 53

a4= 75 + -11*3 = 42

Then the number comes next is a4= 42

krishna-agrawala | Student

Give the following three terms of a series of numbers:

75, 64, 53, ...

If we represent nth term of the series as a(n), then:

a1 = 75

a2 = 64

a3 = 53

Therefore

a2 - a1 = 64 - 75 = - 11

a3 - a2 = 53 - 64 = -11

As the difference between two consecutive terms is common for the three terms, the series can be considered an arithmetical progression with common difference equal to -11.

Therefore:

The next term of the series = a4 = a3 + common difference

= 53 -11 = 42

Answer:

Next term is 42.

eyitopps4real | Student

Just as pohnpe has said, it is an arithmetic progression whose common difference is -11 (obtained by subtracting any two consecutive terms in the sequence). The next term is gotten by adding our common difference to the last term (53) and that gives us 42.

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