Question

The relationship between women’s whole-number shoe sizes and foot lengths is an arithmetic sequence, where an is the foot length in inches that corresponds to a shoe size of n. A women’s size 7 fits a foot mc019-1.jpg inches long, and a women’s size 12 fits a foot 11 inches long. What is the explicit formula for the arithmetic sequence? Round to the nearest hundredth, if necessary.

Answer 1

Answer:

The explicit formula for Arithmetic Sequence is $a_n=7.02+0.33n$

Step-by-step explanation:

Given: Foot length & shoe size in AP.

           $a_n$ is foot length and n is shoe size.i.e., $a_{12}=11\:and\:a_7=9.33$

To find: Formula for Arithmetic sequence .i.e., $a_n$

From question,

$a_{12}-a_7=11-9.33=1.67$

Also, we know that

$a_{12}=a_7+5d\\5d=a_{12}-a_7\\5d=1.67\\d=\frac{1.67}{5}\\\\d=0.33$        

Now, consider

$a_7=a_1+6d\\a_7=a+6d\\a=a_7-6d\\a=9.33-6\times0.33\\a=9.33-1.98\\a=7.35$

Thus using formula of $a_n$ we get,

$a_n=a+(n-1)d\\a_n=7.35+(n-1)\times0.33\\a_n=7.35+0.33n-0.33\\a_n=7.02+0.33n$

Therefore, The explicit formula for Arithmetic Sequence is $a_n=7.02+0.33n$

 

Answer 2

Answer:

an=7.35+ 0.33(n-1)

Step-by-step explanation:

i just took my unit test and that was the answer for that question.