Kenny's score on his 72nd game played is 961
Solution:
Given that the first 5 score of Kenny are listed below:
38, 51, 64, 77, 90
Kenny's scores follow a pattern
To find: Kenny's score on his 72nd game played
Let us first find the pattern followed
38, 51, 64, 77, 90
Find the difference between terms
51 - 38 = 13
64 - 51 = 13
77 - 64 = 13
90 - 77 = 13
So the difference between terms is constant
So the sequence is arithmetic sequence
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant
The formula for nth term of arithmetic sequence is given as:
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]a_n[/tex] = the nᵗʰ term in the sequence
[tex]a_1[/tex] = the first term in the sequence
d = the common difference between terms
Here d = 13 and [tex]a_1 = 38[/tex]
So we get,
[tex]a_n = 38 + (n-1) \times 13[/tex]
To find the score of 72nd game, substitute n = 72
[tex]a_{72} = 38 + (72-1) \times 13\\\\a_{72} = 38 + 71 \times 13\\\\a_{72} = 38 + 923\\\\a_{72} = 961[/tex]
Thus Kenny's score on his 72nd game played is 961
