What is the recursive formula for this arithmetic sequence 3 10 17

Q: What is a recursive function formula?

an= r × an-1 Generally, the recursive function is defined in two parts. It a statement of the first term along with the formula/ rule related to the successive terms.

Key Questions

An arithmetic sequence is a sequence (list of numbers) that has a common difference (a positive or negative constant) between the consecutive terms.
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Here are some examples of arithmetic sequences:
1.)7, 14, 21, 28 because Common difference is 7.
2.) 48, 45, 42, 39 because it has a common difference of - 3.

The following are not examples of arithmetic sequences:
1.) 2,4,8,16 is not because the difference between first and second term is 2, but the difference between second and third term is 4, and the difference between third and fourth term is 8. No common difference so it is not an arithmetic sequence.
2.) 1, 4, 9, 16 is not because difference between first and second is 3, difference between second and third is 5, difference between third and fourth is 7. No common difference so it is not an arithmetic sequence.
3.) 2, 5, 7, 12 in not because difference between first and second is 3, difference between second and third is 2, difference between third and fourth is 5. No common difference so it is not an arithmetic sequence.
#a_n=a_1+(n-1)*d#
#color(white)("XXX")#where #a_1# is the first term and
#color(white)("XXXXXXX")d# is the difference between a term and its previous term.
Examine the pattern:
#a_1#
#a_color(brown)(2)=a_1+d=color(green)(a_1+1d)#
#a_color(brown)(3)=a_2+d=a_1+d+d=color(green)(a_1+2d)#
#a_color(brown)(4)=a_3+d=a_1+2d+dcolor(green)(=a_1+3d)#
#a_color(brown)(5)=a_4+d=a_1+3d+d=color(green)(a_1+4d)#
To find out the common difference in an AP you can perform the following simple step.
Subtract the first term of the AP from the second term of the AP.
d = #a_2 # - # a_1#
where d = common difference
# a_2# = any term other than first term
#a_1# = previous term
For example;
In the AP
3 , 9 , 15 , 21 , 27 , 33
Taking #a_1# = 3
Taking #a_2# = 9
#a_2# - #a_1# = 9 - 3 = 6
hence , common difference or d = 6

Thanks
I hope this helps
The even numbers, the odd numbers, etc
An arithmetic sequence is builded up adding a constant number (called difference) following this method
#a_1# is the first element of a arithmetic sequence, #a_2# will be by definition #a_2=a_1+d#, #a_3=a_2+d#, and so on
Example1:
2,4,6,8,10,12,....is an arithmetic sequence because there is a constant difference between two consecutive elements (in this case 2)
Example 2:
3,13,23,33,43,53,.... is an arithmetic sequence because there is a constant difference between two consecutive elements (in this case 10)
Example 3:

#1,-2,-5,-8,...# is another arithmetic sequence with difference #-3#
Hope this help

We think you wrote:

This solution deals with arithmetic sequences.

Find the common difference

Find the common difference by subtracting any term in the sequence from the term that comes after it.

The difference of the sequence is constant and equals the difference between two consecutive terms.

Find the sum

Calculate the sum of the sequence using the sum formula:

Plug in the terms.

Simplify the expression.

The sum of this sequence is .

This series corresponds to the following straight line

Find the explicit form

The formula for expressing arithmetic sequences in their explicit form is:

Plug in the terms.
(this is the 1st term)
(this is the common difference)
(this is the nth term)
(this is the term position)

The explicit form of this arithmetic sequence is:

Find the recursive form

The formula for expressing arithmetic sequences in their recursive form is:

Plug in the d term.
(this is the common difference)

The recursive form of this arithmetic sequence is:

Find the nth element

Why learn this

When will the next bus arrive? How many people can fit inside a stadium? How much money will I earn this year? All these questions can be answered by learning how arithmetic sequences work. The progression of time, triangular patterns (bowling pins, for example), and increases or decreases in quantity can all be expressed as arithmetic sequences.

Terms and topics

Algebra Examples

What is the recursive formula for arithmetic sequence?

A recursive sequence is a sequence in which terms are defined using one or more previous terms which are given. If you know the nth term of an arithmetic sequence and you know the common difference , d , you can find the (n+1)th term using the recursive formula an+1=an+d .

What is the general rule of the arithmetic sequence with terms 3/10 17 24?

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 7 to the previous term in the sequence gives the next term.

What are the next three terms of the arithmetic sequence 3/10 17 24?

3,10,17,24,31,38,45,52,59,66,73...

What is a recursive function formula?

a_n= r × a_n_-₁ Generally, the recursive function is defined in two parts. It a statement of the first term along with the formula/ rule related to the successive terms.