Answer:
There are 264 poles in the stack.
Explanation:
Number of poles in bottom row = 24
Number of poles in second last row in bottom = 23
Number of poles in top row in bottom = 9
24,23,.....9 (arithmetic sequence)
[tex]a=a_1 = 24[/tex]
[tex]a_2=23[/tex]
d = [tex]a_2-a_2=23-24=-1[/tex]
Number of row in which 9 poles are present be n
the nth term is given by: [tex]a+(n-1)d[/tex]
[tex]9=24+(n-1)(-1)[/tex]
[tex]9=24-n+1[/tex]
[tex]n=16[/tex]
So, there are total 16 rows.
The sum of the nth term in arithmetic sequence is given by :
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]
So, total numbers of poles in stack:
[tex]S_{16}=\frac{16}{2}(2\times 24+(16-1)(-1)=264[/tex]
There are 264 poles in the stack.
