A) The first step needs 100 bricks, the second needs 98, the third needs 96, and so on. Therefore the number of bricks for the nth step is: a_n = a_1 + d(n-1), where a_1 = 100 (the first term), d = -2 (difference).
a_n = 100 - 2(n-1) = 102 - 2n, and for the 30th step, a_30 = 102 - 2*30 = 42. So the top step will need 42 bricks.
b) The total staircase will need: 100 + 98 + 96 + ... + 44 + 42, and there are n = 30 terms. Using the formula for the sum of an arithmetic sequence:
S = (a_1 + a_n)*n/2 = (100 + 42)*30/2 = 2130
Therefore, 2130 bricks are required to build the entire staircase.
Answer:
x= 6, -7
Step-by-step explanation:
Let there be 2x science and 5x art books
<span>science books sold = 2x × 0.2 = 0.4x </span>
<span>science books unsold = 2x – 0.4x = 1.6x </span>
<span>art books sold = 5x × 0.2 = x </span>
<span>art books unsold = 5x – x = 4x </span>
<span>total books unsold = 1.6x + 4x = 5.6x </span>
<span>5.6x = 2240 </span>
<span>x = 400 </span>
<span>2x science = 800 </span>
<span>and 5x art books = 2000 </span>
