The percentage of the non-singing trait in female birds in Generations 4 and 5 if this pattern continues will be 80 and 94
For the given traits, we can see that the singing females form an arithmetic progression as shown:
50, 42, 34...
We need to find the 4th and 5th term
The nth term of an AP is expressed as [tex]T_n = a+(n-1)d\\[/tex]
a is the first term = 50
d is the common difference = 42 - 50 = 34 - 42 = -8
For the 4th term n = 4
[tex]T_4=50+(4-1)(-8)\\T_4=50+3(-8)\\T_4 = 50-24\\T_4 = 26[/tex]
For the fifth term, n = 5
[tex]T_5=50+(5-1)(-8)\\T_5=50+4(-8)\\T_5 = 50-32\\T_5 = 18[/tex]
The percentage of the singing trait in female birds in Generations 4 and 5 if, the pattern continues, is 26 and 18 respectively
For the non-singing females, we can see that 8 was added to the first term to get the second term. 10 was added to the second to get the third
For the 4th term, 12 will be added to the third term;
T4 = 68 + 12
T4 = 80
For the 5th term, 14 will be added to the fourth term;
T5 = 80 + 14
T5 = 94
Hence the percentage of the non-singing trait in female birds in Generations 4 and 5 if this pattern continues will be 80 and 94
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