If there are 20 rows of logs, a. How many logs are there in the bottom row? b. How many logs are there in the pile?

Question

<!--[if !supportLists]-->1.      <!--[endif]-->The top row of a pile of logs contains 7 logs, the row immediately below it has 8 logs, the third row from the top contains 9 logs and so on. If there are 20 rows of logs,

 

<!--[if !supportLists]-->a.       <!--[endif]-->How many logs are there in the bottom row?

 

<!--[if !supportLists]-->b.      <!--[endif]-->How many logs are there in the pile?

Answer 1

First row contains 7 logs. And logs are incrementing by 1 for each successive row. And number of rows is 20.

So using the A.P formula tn = a + (n-1)d we know

a=7, d=1 and n = 20 and we have to find t20, ie number of logs in 20th row.

t20 = 7 + (20 - 1)d

t20 = 7 +19*1

t20 = 26.

a) So there are 26 logs in the bottom row.

Total number of logs is given by the formula Sn = n/2 * [2a + (n-1)]d

So, S20 = 20/2 * [2*7 + (20-1)*1]

S20 = 10 * [ 14+19]

S20 = 10 * 33 = 330

b) So there are total of 330 logs.