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

Question

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.)

Answer 1

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

Answer 2

Whoa...this is really confusing. No idea