Hi,
Write the sum you found using sigma notation
5,-20,80,-320, …
It is geometric series that
a = 5 first term
q = -20/5=-4
s = a ( qn-1) / (q -1)
s = 5 ( (-4)n - 1 ) /( -4-1) = 5 ( (-4)n - 1 ) /( -5) = 1 - ( -4)n
s = ∑ a qk-1 when k = 1 to k = n
OR a + aq + aq2 + aq3 + ... + a qn-1 = 1 - ( -4)n
for better understanding :
if n= 2 it means 5 + (-20) = - 15 then use formula 1 - ( -4)n replace n= 2 the same result
if n= 3 it means 5 + (-20 ) + 80 = 65 then use formula 1 - ( -4)n replace n= 3 the same result
if n= 4 it means 5 + (-20 ) + 80 + ( -320) = - 255 then use formula 1 - ( -4)n replace n= 4 the same result
I hope it is useful,
Minoo
