Algebra 1 help » Functions and Lines » assignment » just how to uncover the nth term of one arithmetic sequence

The an initial term of one arithmetic succession is

*
; the fifth term is
*
. What is the second term?


*


*


*


*


Explanation:

To find the typical difference 

*
, usage the formula
*
.

You are watching: How to find the 100th term

For us,

*
is
*
and
*
is
*
.

*

Now we can solve because that

*
.

*

*

Add the typical difference come the very first term to gain the 2nd term.

*


The amount of the first three terms of an arithmetic succession is 111 and also the fourth term is 49. What is the an initial term?


Explanation:

Let 

*
 be the usual difference, and also let 
*
 be the 2nd term. The an initial three state are, in order, 
*
.

The amount of the very first three terms is

*
.

*

*

Now we know that the 2nd term is 37. The fourth term is the 2nd term plus double the usual difference: 

*
. Because the second and fourth terms space 37 and also 49, respectively, we have the right to solve because that the typical difference.

*

*

*

The typical difference is 6. The first term is 

*
.


Explanation:

For arithmetic sequences, we use the formula 

*
, where 
*
 is the hatchet we space trying come find, 
*
 is the an initial term, and 
*
 is the difference in between consecutive terms. In this case, 
*
 and 
*
. So, we deserve to write the formula as 
*
, and 
*
.


The fourth and tenth regards to an arithmetic sequence room 372 and 888, respectively. What is the very first term?


Explanation:

Let 

*
 be the typical difference of the sequence. Then 
*
, or, equivalently,

*

*
 , or equivalently,

*


The ninth and tenth regards to an arithmetic sequence are, respectively, 87 and 99. What is its an initial term?


Explanation:

The common difference that the sequence is the difference of the tenth and ninth terms: 

*
.

The ninth term of one arithmetic sequence with very first term 

*
 and usual difference 
*
 is 
*
, for this reason we collection this same to 87, set 
*
, and solve:

*

*

*

*


The eighth and also tenth regards to an arithmetic sequence are, respectively, 87 and also 99. What is its an initial term?


Explanation:

The eighth and tenth terms of the succession are 

*
 and 
*
, where 
*
 is the first term and 
*
 is the common difference. We can find the common difference by subtracting the tenth and eighth terms and solving for 
*
:

*

*

*

*

*

 

Now set eighth term 

*
 equal to 87, set 
*
, and solve:

*

*

*

*

*


Before us can number out the 100th term, we need to find a ascendancy for this arithmetic sequence. Remember, the general dominance for this succession is

*

where 

*
to represent the very first number in the sequence, 
*
is the usual difference between consecutive numbers, and 
*
is the 
*
-th number in the sequence.

In ours problem,

*
. Also, each time we move up indigenous one number to another, the number rises by 7. Therefore,
*
. So the dominion for this sequence is composed as

*

Now the we discovered our rule, we have the right to go on and figure out what the 100th hatchet is equal to. Because that the 100th term,

*
. Thus

*

*

*

*


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Example question #8 : just how To uncover The Nth hatchet Of an Arithmetic succession


To find any kind of term of an arithmetic sequence:

*

Where 

*
 is the first term, 
*
 is the variety of the term to find, and 
*
 is the usual difference in the sequence.


Find the 18th term of the complying with arithmetic sequence.

*


Possible Answers:
Correct answer:

*


Explanation:

*

Start by recognize the common difference,

*
, in this sequence, which you can obtain by individually the very first term from the second.

*

Then, using the formula given prior to the question:

*


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Example inquiry #9 : how To uncover The Nth hatchet Of an Arithmetic succession


To find any term of an arithmetic sequence:

*

Where 

*
 is the first term, 
*
 is the number of the term to find, and 
*
 is the usual difference in the sequence.


Find the 26th ax of the following arithmetic sequence.

*


Possible Answers:
Correct answer:

*


Explanation:

*

Start by detect the typical difference in state by subtracting the an initial term native the second.

*

Then, to fill in the rest of the equation given before the question.

*

*


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Example question #8 : just how To find The Nth ax Of an Arithmetic succession


Given the the succession below, what is the 11th ax of the sequence?

1, 5, 9, 13, . . .


Possible Answers:

37


53


45


41


49


Correct answer:

41


Explanation:

The 11th term way there are 10 gaps in in between the first term and also the 11th term. Each void has a difference of +4, for this reason the 11th term would certainly be provided by 10 * 4 + 1 = 41.

The first term is 1.

Each ax after boosts by +4.

See more: Why Do Women Have One More Rib S Does A Woman Have? Women Have More Ribs Than Men

The nth term will be equal to 1 + (n – 1)(4).

The 11th term will be 1 + (11 – 1)(4)

1 + (10)(4) = 1 + (40) = 41


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