Question

Write a recursive definition and an explicit formula for each sequence. Then find a₁₂. 7,13,19,25,31, . . . .

Answer 1

Arithmetic Progression is a recursive mathematical sequence in which the next term is generated by adding the previous term with a fixed number that is called the Common difference represented by 'd'. This is calculated by the difference between any two terms in the given sequence.

The formula to calculate the 12th term of an Arithmetic Progression is :

                                    =>  $a_{12} = a_{(12-1)} + d$    

Here, a = first term, n = nth term, and d = common difference

In the given question, First term a = 7, n = 12, and calculating d,

                                 => $d = a_{2} - a_{1}$  => d = 6

But for a12 we need to find out a11, a10, a9, a8, a7, a6 using the same formula we get :

$a_{6} = 37, a_{7} = 43, a_{8} = 49, a_{9} = 55, a_{10} = 61, a_{11} = 67$

Now for a12 we have a11 = 67, by using formula :

                                  $a_{12} = a_{11} +d$

                                  $a_{12} = 73$

To know more about Arithmetic Progression, Click here :

brainly.com/question/15412619

#SPJ4