Logs are stacked in a pile on the bottom row and 15 on the top row . there are 10 rows in all with each row having one more log that the one above it. how many logs are in the stack?

Since there is a common difference of one, this is an arithmetic sequence of the form a(n)=a+d(n-1) which in this case is:

a(n)=15+1(n-1)

All arithmetic sequences have a sum which is equal to the average of the first and last terms time the number of terms, mathematically:

s(n)=(2an+dn^2-dn)/2  (that is just the result of ((a+a+d(n-1))(n/2)) )

Since a=15 and d=1 this becomes:

s(n)=(30n+n^2-n)/2

s(n)=(n^2+29n)/2 so

s(10)=(100+290)/2

s(10)=195 logs