Question

The number of corn stalks in each row of field can be modeled by arithmetic sequence.The 5th row in this field has 36 corn stalks. The 12th row in the field has 64 stalks. Write an explicit rule for an arithmetic sequence that models the number of stalks s in the nth row of the field. show your work

Answer 1

Answer:

a_{n}=20+4(n-1)

Step-by-step explanation:

It is given that the number of corn stalks in rows of the field can be modeled by an arithmetic sequence.

The 5th row has 36 corn stalks. This means 5th term of the sequence is 36. i.e.

$a_{5}=36$

The 12th row has 64 stalks. So,

$a_{12}=64$

In order to write the explicit rule we need to find the first term(a1) and common difference(d) of the sequence.

The explicit rule for the arithmetic sequence is of the form:

$a_{n}=a_{1}+(n-1)d$

Writing the 5th and 12th term in this way, we get:

$a_{5}=a_{1}+4d$

$a_{1}+4d=36$                                                     Equation 1

Similarly for 12th term, we can write:

$a_{1}+11d=64$                                                     Equation 2

Subtracting Equation 1 from Equation 2, we get:

7d = 28

d = 4

Using the value of d in Equation 1, we get:

$a_{1}+4(4)=36\\\\ a_{1}=20$

Thus, for the given sequence first term is 20 and common difference is 4. Using these values in the general explicit rule, we get:

$a_{n}=20+4(n-1)$