Question

A wall is in the shape of a trapezium. The first level of the wall is made up of 50 bricks where as the top level has 14 bricks. If the levels differ from each other by 4 bricks, determine the number of;
(i)levels of the bricks.
(ii)bricks used to make the wall.​

Answer 1

Answer:

i). 10 levels of the bricks

ii). 320 bricks

Step-by-step explanation:

First level contains number of bricks = 50

Second level will contain = 50 - 4 = 46 bricks

Similarly, 3rd level will contain number of bricks = 46 - 4 = 42

Therefore, sequence formed for the number of bricks in each level of the wall will be,

50, 46, 42........14

This sequence is an arithmetic sequence having,

First term 'a' = 50

Common difference 'd' = 46 - 50 = (-4)

Last term of the sequence $T_{n}$= 14

i). Expression representing last term will be,

  $T_{n}=a+(n-1)d$

  Here $T_{n}$ = nth term

  a = first term

  n = number of term (Number of level of the wall)

  d = common difference

  By substituting these values in the formula,

  14 = 50 + (n - 1)(-4)

  14 - 50 = (-4)(n - 1)

  -36 = -4(n - 1)

  9 = (n - 1)  

  n = 9 + 1

  n = 10

ii). Number of bricks used in the wall = Sum of the sequence

   Expression for the sum of an arithmetic sequence is,

   $S_n=\frac{n}{2}[2a+(n-1)d]$

   $S_n=\frac{10}{2}[2\times 50+(10-1)(-4)]$

        = 5(100 - 36)

        = 320 bricks