Question

What’s the 38th term of the arithmetic sequence 31,40,49,58?

Answer 1

Answer:

$a_3_8=364$

Step-by-step explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference

we have

$31,40,49,58,...$

Let

$a_1=31\\a_2=40\\a_3=49\\a_4=58$

we have that

$a_2-a_1=40-31=9$

$a_3-a_2=49-40=9$

$a_4-a_3=58-49=9$

so

The common difference is equal to 9

We can write an Arithmetic Sequence as a rule:

$a_n=a_1+d(n-1)$

where

a_n is the nth term                                                              

a_1 is the first term

d is the common difference                        

n is the number of terms

Find the 38th term of the arithmetic sequence

we have                  

$a_1=31\\d=9\\n=38$              

substitute the values

$a_3_8=31+9(38-1)$

$a_3_8=31+9(37)$

$a_3_8=364$