Question

Use the recursive formula to answer the question.
a1=12
an=an−1+4

What is the 7th

term in the sequence?

Enter your answer as a number, like this: 42

Answer 1

You know a1.
So find a2, a3, and so on until a7.

a(1) = 12
a(2) = 16
a(3) = 20
a(4) = 24
a(5) = 28
a(6) = 32
a(7) = 36
Each is 4 more than the previous.

Answer 2

The 7th term ( $a_{7}$ ) in the sequence is 36.

The given recursive formula is given as:

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

We are also given,

The first term = 12.

We need to find the value of the 7th term in the sequence using the given recursive formula.

We will denote the sequence as  $a_{1},~a_{2},~ a_{3},~a_{4}$,...........

So we have,

$a_{1}$ = 12.

Now,

Using the recursive formula we will find the 7th term in the sequence.

We can not directly find the 7th term in the sequence because we need the 6th term.

i.e  $a_{7} = a_{6} + 4$

So we need to find each value till the 6th term to get the 7th term.

First term -

$a_{1}$ = 12

Second term -

$a_{2} = a_{1} + 4$ = 12 + 4 = 16

Third term -

$a_{3} = a_{2}$ + 4 = 16 + 4 = 20

Fourth term -

$a_{4} = a_{3}$ + 4 = 20 + 4 = 24

Fifth term -

$a_{5} = a_{4}$ + 4 = 24 + 4 = 28

Sixth term -

$a_{6} =a_{5}$ + 4 = 28 + 4 = 32

7th term -

$a_{7} = a_{6}$ + 4 = 32 + 4 = 36

We see that the sequence is 12, 16, 20, 24, 28, 32, 36.

Thus the 7th term ( $a_{7}$ ) is 36.

Learn more about the sequence with recursive formula here:

https://brainly.com/question/17549356

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