What does the 1/2 in Sn = n/2*(a1 + an) represent?

Question

anonymous · Answer

$$s _{n}=_{2}^{n}(a_{1}+a _{n}) $$

What does the 2 under  the n represent?

apoorvk · Answer

2 represents "2" . the no. two. what else?

it comes from the fact that when adding up, every first and last nos.' "average" is being taken into account, before being added n times.

anonymous · Answer

The $$s _{n} $$ represents the sum up to the nth term correct?

The $$a_{1}$$
Represents the first term correct?

The $$a_{n}$$
represents the a to the nth term correct?

campbell_st · Answer

a simple example is 

find the sum of 1, 2, 3, 4

 you can arrange  the numbers and add pairs 

       1 2 3 4
 +    4 3 2 1 
-----------
        5 5 5 5 

each pair sums to the same thing... and there are 2 sets of numbers 

 4 lots of 5

to find the sum halve the product of 4 and 5

(4 x 5)/2 = 10    the sum.... works for all arithmetic series