How many black and how many red counters are there in a triangular array like this but with 20 rows?

A: How many black and how many red counters are there in a triangular array like this but with 20 rows?





 - Black


 -Red


 -Black


 -Red


 -Black





You should not actually need to make a diagram with 20 rows in order to answer this question.





B: Write a brief explanation of your solution to part (a).





C: Repeat part (a) but with a triangular array with 21 rows.





D: What integers are represented by the triangular arrays in parts (a) and (c)?





E: Make a table of integers represented by triangular arrays like those in parts (a) and (c), but with n rows for n=1, 2, 3, 4, 5, 6, 7, and 8.





F: Carefully considering the table of part (e), conjecture what integer is represented in a triangular array like those in parts (a) and (c), but with n rows, where n is any natural number (Suggestion: Consider n odd and n even separately.)

How many black and how many red counters are there in a triangular array like this but with 20 rows?
use arithmatic progression formula n(2a+(n-1)d)/2


where n=no. of terms. a=value of first term and d=common difference between each consecutive term


say fro your first eg. no. of black ball = 1+3+5+...


n=10 a=1 d=2


so sum = 10(2+9*2)/2 = 100


solve the rest by changing values of n, a and other variables respectively
Reply:Whoa...this is really confusing. No idea

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