Question

stack of poles has 24 poles in the bottom row, 23 poles in the next row, and so on, with 9 poles in the top row. How many poles are there in the stack?

Answer 1

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)

$a=a_1 = 24$

$a_2=23$

d = $a_2-a_2=23-24=-1$

Number of row in which 9 poles are present be n

the nth term is given by: $a+(n-1)d$

$9=24+(n-1)(-1)$

$9=24-n+1$

$n=16$

So, there are total 16 rows.

The sum of the nth term in arithmetic sequence is given by :

$S_n=\frac{n}{2}(2a+(n-1)d)$

So, total numbers of poles in stack:

$S_{16}=\frac{16}{2}(2\times 24+(16-1)(-1)=264$

There are 264 poles in the stack.