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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 = 14
i). Expression representing last term will be,
Here = 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,
= 5(100 - 36)
= 320 bricks