Expert answers to "Caitlins"

High School
Algebra
Algebra I
Exponents and radicals

Yasmin

Answered question

2021-03-06

Caitlins

Answer & Explanation

FieniChoonin

Skilled2021-03-07Added 102 answers

The numbers are given as follows.
$a_{1} = 75, a_{2} = 68, a_{3} = 70, a_{4} = 63, a_{5} = 65, a_{6} = 58, a_{7} = 60, \dots$
We have to find the rule for the pattern. Notice that the first number is 75 and the second number is 68. Note that
$a_{2} = 68 = 75 - 7 = a_{1} - 7$
Now the third number is 70 which can be written as
$a_{3} = 70 = 68 + 2 = a_{2}^{2} + 2$
Now note that a4=63 which can be expressed as
$a_{4} = 63 = 70 - 7 = a_{3} - 7$
Now we have a5=65 which can be represent as
$a_{5} = 65 = 63 + 2 = a_{4} + 2$
Therefore the given number can be expressed as follows
$a_{1} , a_{2} = a_{1} - 7, a_{3} = a_{2} + 2, a_{4} = a_{3} - 7, a_{5} = a_{4} + 2, \dots$
Hence the pattern is
Subtract 7, add 2(Correct Choice: C)

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