Arithmetic Sequences

Question

Find the sum: 5+3+1+...+(7−2n)

Answer 1

5+3+1 -1 -3 -5 -7 -9 ...(7-2n)...

Sn = (n/2)(2a +(n+1)d

where d=common difference, in this example d=-2

or

Sn = (n/2)(a+an) where an is the last term in the finite series

the sum of the first 6 terms is

S6 = (6/2)(2(5) + (6-1)(-2)) = 3(10-10) = 0

or

S6 =(n/2)(5-5) = 0

for another number of terms, substitute another number for n into the equation

if you want to sum an infinite number of terms, there is no real solution, it just approaches negative infinity