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 Question from Daphne, a student: Hi, My name is Daphne and I am having trouble with a math problem. I am given this pattern below and asked to find an expression for the number of Bs in the nth term of the pattern. Someone please help!!! ABBA AABBBAA AAABBBBAAA AAAABBBBBAAAA The next part asks me to find the ratio of Bs to total letters in the nth term. Finally it says to use my expression to determine which term has exactly 35% Bs. HELP!!!!

Hi Daphne,

I would set up a table with the row number in the first column, the number of Bs in that row in the second column and the number of letters in that row in the third column. This gives me

Row Bs Letters
1 2 4
2 3 7
3 4 10
4 5 13
5

If you continue the pattern how many Bs will be in row number 5? What about row number 9? How about row number n? This is the expression for the number of Bs in the nth term of the pattern.

Can you also find an expression for the number of letters in row number n?

Penny

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