a. One row contains 17 bricks. Which row is this? b. How many rows of bricks are there? Explain your assumptions. A pile of bricks is...

The given arithmetic sequence is:

65, 59, 53 ...

This can be expressed as:

(6*11 -1), (6*10 -1), (6*9 -1), ... (6*5 -1),(6*4 -1), (6*3 -1)

Pleas not that in the above series the last number is 17 which is assume to be the number of bricks in last row in pile of bricks. This give total of 9 term or rows in the series.

The above series can be further rewritten as:

(6*8) + (6*3 -1), (6*8) + (6*3 -1), (6*7) + (6*3 -1), ... (6*2) + (6*3 -1), (6) + (6*3 -1), (0) + (6*3 -1)

= (6*8) + 17, (6*7) + 17, (6*6) + 17, ... (6*2) + 17, 6 + 17, 17

Thus addition of all the eleven terms in the series is equal given by:

= (6*8) + (6*7) + (6*6), ... + (6*2), 6, + 0

+ 17  + 17     + 17             + 17  + 17 + 17

= [6 (8 +7 + 6 + ... + 3 +2 + 1] + (9*17)

= 6*36 + 153 = 216 + 153 = 369

Answer:

When the last row contains 17 bricks, there will be 9 rows.

Total number of bricks = 369