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Arithmetic Sequences & Series 1
Contributed by: Potter

The common difference.

Find:

For the following sequence:  9,   13,   17,   21, ...

The rule for the nth term.  an =

The indicated term.  a38 =

The next three terms.

in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
,
add4
add4
,
add4
Finding "the rule":an = a1 + (n-1)•dan = 9 + (n-1)•4        9 + 4n - 4an = 5 + 4n
this is simplified form
Finding a38:a38 = 5 + 4•(38)a38 = 5 + 152a38 = 157

The common difference.

Find:

For the following sequence: 18,  16,   14,   12, ...

The rule for the nth term.  an =

The indicated term.  a25 =

The next three terms.

in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
,
sub2
sub2
,
sub2
Finding "the rule":an = a1 + (n-1)•dan = 18 + (n-1)•-2        18 - 2n + 2an = 20 - 2n
this is simplified form
Finding a25:a25 = 20 - 2•(25)a25 = 20 - 50a25 = -30

The common difference.

Find:

For the following sequence:  1,   7,   13,   19, ...

The rule for the nth term.  an =

The indicated term.  a28 =

The next three terms.

in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
,
,
Finding "the rule":an = a1 + (n-1)•d

The common difference.

Find:

For the following sequence:  −13,   −11,   −9,   −7, ...

The rule for the nth term.  an =

The indicated term.  a40 =

The next three terms.

in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
,
,
Finding "the rule":an = a1 + (n-1)•d

The common difference.

Find:

For the following sequence: 11,   15,   19,   23, ...

The rule for the nth term.  an =

The indicated term.  a40 =

The next three terms.

in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
,
,
Finding "the rule":an = a1 + (n-1)•d

The common difference.

Find:

For the following sequence: 6,   −2,   −10,   −18, ...

The rule for the nth term.  an =

The indicated term.  a29 =

The next three terms.

in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
,
,
Finding "the rule":an = a1 + (n-1)•d

The rule for the nth term.  an =

Given: A term in an arithmetic sequence and the common difference.

a17 = 57, d = 3

Find:

The next three terms.

Write the rule in simplified form:an = a1 + (n-1)•dan = 9 + (n-1)•3
in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
an = 9 + 3n - 3
an = 6 + 3n
,
,
Finding "the rule":an = a1 + (n-1)•dFind a1 first  a17 = a1 + (n-1)•d  57 = a1 + (17-1)•3  57 = a1 + (16)•3  57 = a1 + 48-48          - 48
9 = a1

The rule for the nth term.  an =

Given: A term in an arithmetic sequence and the common difference.

a14 = -136, d = -8

Find:

The next three terms.

Write the rule in simplified form:an = a1 + (n-1)•dan = -32 + (n-1)•-8
in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
an = -32 - 8n + 8an = -24 - 8n
,
,
Finding "the rule":an = a1 + (n-1)•dFind a1 first  a14 = a1 + (n-1)•d-136 = a1 + (14-1)•-8-136 = a1 + (13)•-8-136 = a1 - 104+104         +104
-32 = a1

The rule for the nth term.  an =

Given: A term in an arithmetic sequence and the common difference.

a15 = 272, d = 20

Find:

The next three terms.

in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
,
,

The rule for the nth term.  an =

Given: A term in an arithmetic sequence and the common difference.

a34 = 26, d = 2

Find:

The next three terms.

in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
,
,

The rule for the nth term.  an =

Given: A term in an arithmetic sequence and the common difference.

a26 = -66, d = -4

Find:

The next three terms.

in simplified form:  (like an = 5+4n) 
Arithmetic Sequences & Series
,
,

Find a10 =

Identify a1:

Find the sum if the first "n" terms of the indicated series.

4 + 8 + 12 + 16...          n = 10

Use the sum formula to find the sum.

=
Arithmetic Sequences & Series
10•(4+40)
2
=
440
2
=
220
Finding "an":a10 = a1 + (n-1)•da10 = 4 + (10-1)•4          4 + (9)•4a10 = 40

Find a12 =

Identify a1:

Find the sum if the first "n" terms of the indicated series.

25 + 34 + 43 + 52...      n = 12

Use the sum formula to find the sum.

Arithmetic Sequences & Series
Finding "an":an = a1 + (n-1)•d

Find a1 =

Find a10 =

Use the sum formula to find the sum.

Find the sum of the series using summation notation.

Arithmetic Sequences & Series
This is an. Use it to find a1 & a10.
Finding "a1":an = 2i + 4a1 = 2(1) + 4 = 6
Finding "a10":an = 2i + 4a10 = 2(10) + 4 = 24

Find a1 =

Find a7 =

Use the sum formula to find the sum.

Find the sum of the series using summation notation.

Arithmetic Sequences & Series
This is an. Use it to find a1 & a7.
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