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Jeff Bivin -- LZHS
Arithmetic Sequences
Last UpdatedApril 4, 2012
Arithmetic Sequences
5, 8, 11, 14, 17, 20, … 3n+2, …
-4, 1, 6, 11, 16, … 5n – 9, . . .
11, 7, 3, -1, -5, … -4n + 15, . . .
General term or nth term of an arithmetic sequence
an = a1 + (n – 1)d
Find the general term of an arithmetic sequence
First term is 8
Common difference is 3
an = a1 + (n – 1)d
an = 8 + (n – 1)3
an = 8 + 3n – 3
an = 3n + 5
Find the general term
First term is 23
Common difference is -4
an = a1 + (n – 1)d
an = 23 +(n – 1)(-4)
an = 23 - 4n + 4
an = -4n + 27
Find the 100th term5, 11, 17, 23, 29, . . .
an = a1 + (n – 1)d
a100 = 5 + (100 – 1)6
a100 = 5 + 6(99)
a100 = 5 + 594
a100 = 599
a1 = 5
d = 6
n = 100
Find the general term and a recursive formula
4th term: 108 956th term: -15124
108 = a1 + 3d
-15124 = a1 + 955d
So…. d = -16 and a1 = 156
General term: Recursive formula:
an = 156 +(n-1)(-16) an = an-1 -16
an= -16n + 172
Summing it up(adding the terms of an arithmetic sequence)
)(2 1
1n
n
kkn aa
naS
Find the sum of the first 7 terms: 1 , 4 , 7 , 10 , 13 , 16 , 19,
…
a1 = 1
an = 19
n = 7
)(2 1 nn aan
S
)191(2
77 S
2
)20(77 S
707 S
Find the sum of the first 5 terms and the first n terms. 1, 3, 5, 7, 9, …2n-1
)(2 515 aan
S
2
)91(55
S
2
)10(55 S
255 S
)(2 1 nn aan
S
)121(2
nn
Sn
)2(2
nn
Sn
2nSn
Find the sum of the integers from 1 to 100
a1 = 1
an = 100
n = 100
2
)( 1 nn
aanS
2
)1001(100100
S
2
)101(100100 S
5050100 S
Find the sum: 8+11+14+17…+ (3n+5)
a1 = 8
an = 3n+5)538(
2 n
nSn
)658(2
2020 S
73020 SJeff Bivin -- LZHS
)133(2
nn
Sn
Find the sum of the first 20 terms:
73020 S
OR 13)20(32
2020 S
Find the sum: 5 + 9 + 13 + … + 49
a1 = 5
an = 49
d = 4
n = ?
2
)( 1 nn
aanS
2
)495( n
Sn
2
)54(1212 S
32412 S
dnaan )1(1 4)1(549 n
4444 nn448 n12
Find the sum: 13 + 15 + 17 +…+ 47
a1 = 13
an = 47
d = 2
n = ?
2
)( 1 nn
aanS
2
)4713( n
Sn
2
)60(1818 S
54018 S
2)1(1347 n
n18
Evaluate
a1 = -29
an = -199
d = -2
n = 862
)( 1 nn
aanS
2
)19929(86 nS
2
)228(86 nS
9804nS
Sn = -29 - 31 - 33 + . . . - 199
100
15
)12(k
k
Review – Arithmetic Sequences
nth term Sum of n terms
dnaan )1(1 )(
2 1 nn aan
S
