Please Help!! Math
posted by Jnr John on .
A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans. How many cans, in total, are in the display?

terms of the sequence:
20 , 18 , 16 ,...4
So we have a = 20, d = 2 , t(n) = 4
t(n) = a + (n1)d
4 = 20 + (n1)(2)
16 = 2n + 2
2n = 18
n = 9
so we need sum of 9 terms
= (9/2)(first + last)= (9/2)(20 + 4) = 108
or
Sum(n) = (n/2)(2a + (n1)d)
= (9/2)(40 + 8(2)) = 108
check:
term9 = a = 8d
= 20 + 8(2) = 2016 = 4