When finding the sum of the arithmetic series 4 + 1 + –2 + –5 + –8 + –11, you will have a step of work that contains the number –3. Use complete sentences to describe how the –3 was calculated and what it means.

Question

anonymous · Answer

We notice that the difference between a following term and its preceding term is -3, therefore, between each term, we recursively add -3 to reach the next term.

campbell_st · Answer

the 1st term in the sequence is a = 4

find the common difference, which means the difference between terms is always the same.  

$$a_{2} - a_{1} = a_{3} - a_{2} = a_{4} - a_{3} = ...$$

there are 6 terms in your sequence.... 

there are several formulae that can be used

$$S_{n} = \frac{n}{2}[ 2a + (n - 1)d]$$      
n = number of terms, a = 1st term, d = common difference

A term in the series can be found using 

$$T_{n} = a + (n - 1)d$$

so the above formula can be written as

$$S_{n} = \frac{n}{2}[ a +  a + (n - 1)d]$$  

or 

$$S_{n} = \frac{n}{2}[ a + l] $$   l = last term

a simple way to solve this problem is is reverse the order and add the 2 sets of numbers together

        4,   1, -2, -5, -8, -11
+   -11,-8, -5,  -2,   1,    4
-------------------------
       -7, -7, -7, -7, -7, -7

there are 6 lots of - 7     which sum to - 42

becuase you doubled the sets of numbers halve your answer

-42/2 = -21

this is both formulae is a simple style.