Posted by **Jnr John** on Tuesday, April 16, 2013 at 11:29pm.

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?

- Please Help!! Math -
**Reiny**, Tuesday, April 16, 2013 at 11:36pm
terms of the sequence:

20 , 18 , 16 ,...4

So we have a = 20, d = -2 , t(n) = 4

t(n) = a + (n-1)d

4 = 20 + (n-1)(-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 + (n-1)d)

= (9/2)(40 + 8(-2)) = 108

check:

term9 = a = 8d

= 20 + 8(-2) = 20-16 = 4

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