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.

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.

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, . . .

37

53

45

41

49

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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