Question

What is the recursive formula for this sequence? 12, 16, 20, 24, 28, ...

Answer 1

Answer:

Option A is correct.

$a_1 = 12$

$a_n = a_{n-1}+4$

Step-by-step explanation:

For a sequence $a_1, a_2, a_3, . . . , a_n, . . .$

A recursive formula states that it is a formula that requires the computation of all previous terms in order to find the value of $a_n$ i,e  it is given by;

$a_n = a_{n-1}+d$                    ......[1]

Given the sequence : 12, 16, 20, 24, 28, .......

here,

First term = $a_1 = 12$

$a_2 = 16$

$a_3 = 20$

$a_4 = 24$ and so on....

Now, find the common difference(d);

Common difference states that it is the difference between two numbers in an arithmetic sequence

Therefore, from the given sequence ;

d = 4

Since,

16 -12 = 4,

20-16 =4,

24 -20 = 4 and so on.....

Now, substitute the value of $a_1 = 12$ and d =4 in [1] ; we get

$a_n = a_{n-1}+4$

Therefore, we have;

$\left\{{{a_1=12} \atop {a_n =a_{n-1}+4}} \right$

Answer 2

The answer is A, recursion uses the previous answer to solve the next answer so:

If a sub 1 is 12

Then a sub 2 = 12 + 4 = 16
Therefore a sub n = a sub (n - 1) + 4