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10.2 Arithmetic Sequences. Date: ____________. Arithmetic Sequence. Sequence in which each term after the first is obtained by adding a fixed number, called the difference, to the previous term. +3. +3. +3. +3. Common difference is 3. 5, 8, 11, 14, 17,. (d = 3). -2. -2. -2. -2. - PowerPoint PPT Presentation
10.2Arithmetic Sequences
Date: ____________
Arithmetic Sequence
• Sequence in which each term after the first is obtained by adding a fixed number, called the difference, to the previous term.
5, 8, 11, 14, 17, . . .
+3 +3 +3 +3
16, 14, 12, 10, 8, . . .
-2 -2 -2 -2
Common difference is 3.
(d = 3)
Common difference is -2.
(d = -2)
Decide if each sequence is an arithmetic sequence. If yes, find the
common difference.
-5, -1, 3, 7, 11,... Yes. d = 4
4, 5, 7, 10, 14,… No.
1, 4, 8, 12, 16,… No.
-4, -7, -10, -13, -16,… Yes. d = -3
Arithmetic Sequence
an = a1 + d(n − 1)
an = nth term of the sequence
a1 = first term
n = # of terms
d = common difference
Find an and a20.
a1 = 7 d = 5
an = 7 + 5(n − 1)
an = 7 + 5n – 5
an = 2 + 5n
a20 = 2 + 5(20)
a20 = 102
an = a1 + d(n − 1)
Find an and a25.
48, 53, 58, 63,… an = a1 + d(n − 1)
48 5an = 48 + 5(n – 1)
an = 48 + 5n – 5
an = 43 + 5n
a25= 43 + 5(25)
a25 = 168
Find an and a25.
-21, -39, -57, -75,… an = a1 + d(n − 1)
-21 -18
an = -21 – 18(n – 1)
an = -21 – 18n + 18
an = -3 – 18n
a25= -3 – 18(25)
a25 = -453
Find an and a20.
a17 = 22 d = -4
an = a1 + d(n − 1)
22 = a1 – 4(17 − 1)
22 = a1 – 4(16)
22 = a1 – 64
86 = a1
an = 86 – 4(n − 1)
an = 86 – 4n +4
an = 90 – 4n
a20 = 90 – 4(20)
a20 = 10
Find an and a13.
a15 = 10 a20 = 25 d =25 – 10
20 – 15 =
15
5 = 3
an = a1 + d(n − 1)
10 = a1 + 3(15 − 1)
10 = a1 + 3(14)
10 = a1 + 42
-32 = a1
an = -32 + 3(n − 1)
an = -32 + 3n – 3
an = -35 + 3n
a13 = -35 + 3(13)
a13 = 4
Find an and a13.
a12 = -23 a27 = 37 d =37 − ‾23
27 – 12
=60
15 = 4
an = a1 + d(n − 1)
-23 = a1 + 4(12 − 1)
-23 = a1 + 4(11)
-23 = a1 + 44
-67 = a1
an = -67 + 4(n − 1)
an = -67 + 4n – 4
an = -71 + 4n
a13 = -71 + 4(13)
a13 = -19
Sum of a Finite Arithmetic Sequence
2
+= 1 n
n
aanS ( )
Find the sum of the first 10 terms of the sequence if a1 = -16 and a10 = 20
2
20+1610=10S ( ) S10 = 20
Find the sum of the first 42 terms of the sequence if a1 = 7 and a42 = 239
( )2
239+742=42S
S42 = 5166
2
+= 1 n
n
aanS ( )
Find the sum of the first 100 terms of the sequence if a1 = 5 and d = 3.
2
+100= 1001
100
aaS ( ) an = a1 + d(n − 1)
a100 = 5 + 3(100 − 1)
a100 = 3022
302+5100=100S ( )
S100 = 15,350
Find the sum of the first 24 terms of the sequence if a1 = -4 and d = -6.
2
+24= 241
24
aaS ( ) an = a1 + d(n − 1)
a24 = -4 – 6(24 − 1)
a24 = -1422
421+424=24S ( )S24 = -1752
Find the sum of the first 50 terms of the sequence 34, 45, 56, 67, 78,…
2
+50= 501
50
aaS ( ) a50 = 34 + 11(50 − 1)
a50 = 573
2
573+3450=50S ( )
S50 = 15,175
an = a1 + d(n − 1)
Find the sum of the first 20 terms of the sequence 12, 18, 24, 30, 36,…
2
+20= 201
20
aaS ( ) a20 = 12 + 6(20 − 1)
a20 = 126
2
126+1220=20S ( )
S20 = 1380
an = a1 + d(n − 1)