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#### Online Quiz (WorksheetABCD)

Questions Per Quiz = 2 4 6 8 10

### High School Mathematics - 23.2 Arithmetic Sequence

Arithmetic Sequence
• Is a sequence such as 3,7,11,15,.....99 or 5,10,15,20,25.....2000 which has a constant difference between terms.
• The first term is written as a1,
• The 5th term is written as a5,
• The 10th terms is written as a10 and
• The difference is written as d.
 Term Number 1 2 3 4 ..... n Term of Arithmetic Series a1 a2 a3 a4 ..... an Term of Arithmetic Series a1 a1 + d a1 + 2d a1 + 3d ..... an + (n-1)d Example 2 6 10 14 ..... 2 + (n-1)4

a1
a2 = a1 + d
a3 = a2 + d = (a1 + d) + d = a1 + 2d
a4 = a3 + d = (a2 + d) + d = a1 + 3d
a5 = a1 + 4d
a6 = a1 + 5d
a7 = a1 + 6d
........
an = a1 + (n-1)d

The formula to find the nth term in Arithmetic series is
 a + (n-1)d

Example: 2, 6, 10, 14 ..........
Here
d = a2 - a1 = 4
a1 =2
a2 = 6
a3 = 10
a4 = 14
a5 = 18
a10 = 38
a101 = a + (n-1)d = 2 + (101-1)4 = 2 + 100 x 4 =2 + 400 = 402

Directions: Find d, a1, a5 or a101 for the following arithmetic sequence. Also write at least 5 examples of your own.
 Q 1: Find d, a1, a5 for the following arithmetic sequence: 5, 8, 11, 14, 17...............3n+2d=3,a1=5, a5= 20d=5,a1=2, a5= 20d=4,a1=5, a5= 18 Q 2: Find d, a1, a5 for the following arithmetic sequence: 2,-3,-8,-13,...............7-5nd=-4, a1=7, a5= -23d=-5, a1=2, a5= -18d=5, a1=7, a5= 13 Q 3: Find d, a1, a5, a101 for the following arithmetic sequence: 1,4,7,10,13,16,..............d = 3, a1=1, a5= 13, a10=28,a101=301d = 5, a1=1, a5= 15, a10=28,a101=301d = 3, a1=1, a5= 23, a10=38,a101=201 Q 4: Find d, a1, a5 for the following arithmetic sequence: 1,5/4,3/2,7/4,...............(n+3)/4d=1/4,a1=1, a5= 2d=1/3,a1=1, a5= 2/3d=1/4,a1=1, a5= 8/5 Q 5: Find d, a1, a5 for the following arithmetic sequence: a, a+2, a+4, a+6..............2n+a-2d=n,a1=a, a5= n+8d=a,a1=a, a5= n+8d=2,a1=a, a5= a+8 Q 6: Find d, a1, a5, a101 for the following arithmetic sequence: 3,0,-3,-6,-9,-12,................d = -3, a1=3, a5= -9, a10=-24, a101= 296d = -2, a1=3, a5= -8, a10=-24, a101= 296d = 3, a1=3, a5= -9, a10=-24, a101= 296 Q 7: Find d, a1, a5 for the following arithmetic sequence: 7,11,15,19,...............4n+3d=4, a1=7, a5= 23d=3, a1=7, a5= 22d=5, a1=7, a5= 24 Q 8: Find d, a1, a5, a101 for the following arithmetic sequence: -1,10,21,32,43,54,.................d = 11, a1=-1, a5= 43, a10=98,a101=1099d = 9, a1=-1, a5= 45, a10=99,a101=1199d = 10, a1=-2, a5= 44, a10=88,a101=999 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!