Explanation:
Question 2) Answer
Use Arithmetic Series Formulas:
a) Nth term = F + (N - 1) x D, where F=First term, N=Number of terms, D=Common difference
6th row = 23 + (6 - 1) x -3
= 23 + (5) x -3
= 23 + (-15)
= 8 - number of boxes in the top row.
b) Sum = N/2[2F + (N - 1) x D]
= 6/2[2*23 + (6 - 1) x -3]
= 3 [46 + (5) x -3 ]
= 3 [46 + -15 ]
= 3 [ 31 ]
= 93 - total number of boxes in the entire display.
Question 3) Answer
Sum of the 8 first terms of the geometric progression with the first term 50 and the common ratio of 2:
=50 + 5*2 + 50*2^2 + . . . + 50*2^7
= 50*(1 + 2 + 2^2 + . . . + 2^7) = 50*(2^8-1)
= 50*(256-1) = 50*255
= 12750 Answer
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