Question 1189816
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As you see, and it is almost obvious, this sequence is an arithmetic progression.

The first term is 12 and the common difference is -5.


On the number line, the distance between the first term and the last term is 

    12 + 203 = 215.


The number of gaps between the terms in the number line is  {{{215/5}}} = 43.


Add 1 (one) to it, and you will get the number of terms of the progression: it is 43 + 1 = 44.    <U>ANSWER</U>


It is the simplest way to solve this and hundreds other similar problems.


Your intuition and your common sense will dictate you what to do . . . without memorizing any formulas.


<U>CHECK</U>.   To check, calculate the last term, using standard formula of an arithmetic progression


         {{{a[44]}}} = {{{a[1] + (44-1)*d}}} = 12 - 43*5 = - 203.    ! Correct !
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Solved.