Tricky sequences and series question

• Nov 18th 2008, 01:49 AM
nerdzor
Tricky sequences and series question
A timber worker is stacking logs. the logs are stacked in layers, where each layer contains one log less than the layer below. There are five logs in the top layer, six logs in the next layer and so on. There are n layers altogether.

a. Write down the number of logs in the bottom layer

b. Show that there are $\displaystyle \frac{1}{2} n(n+9)$ logs in the stack
• Nov 18th 2008, 06:36 AM
cosine
a) There are a+(n-1)d logs in the nth layer, with 'a' referring to the first number in the sequence (5) and 'd' referring to the common difference (1). n refers to the layer which you are looking at.

5+(n-1)1 = 5+n-1 = n+4

to prove > we know the third layer will have 7 logs in. 3+4 = 7

b) Here you must use the equation for finding the sum of the terms in an arithmetic sequence.

a=5
d=1
n=?
Sn=?

Sn=1/2n [2a + (n-1)d]
Sn=1/2n [10 + (n-1)1]
Sn=1/2n [10 + n - 1]
Sn=1/2n [n + 9]

There she blows