what is the word description of the sequence: 21,23,25,27,29?
Answers
Answer:
21,23,25,27,29,31,33,35
Your input 21,23,25,27,29,31,33,35 appears to be an arithmetic sequence
Find the difference between the members
a2-a1=23-21=2
a3-a2=25-23=2
a4-a3=27-25=2
a5-a4=29-27=2
a6-a5=31-29=2
a7-a6=33-31=2
a8-a7=35-33=2
The difference between every two adjacent members of the series is constant and equal to 2
General Form: an=a1+(n-1)d
an=21+(n-1)2
a1=21 (this is the 1st member)
an=35 (this is the last/nth member)
d=2 (this is the difference between consecutive members)
n=8 (this is the number of members)
Sum of finite series members
The sum of the members of a finite arithmetic progression is called an arithmetic series.
Using our example, consider the sum:
21+23+25+27+29+31+33+35
This sum can be found quickly by taking the number n of terms being added (here 8), multiplying by the sum of the first and last number in the progression (here 21 + 35 = 56), and dividing by 2:
n(a1+an)2
8(21+35)
2
The sum of the 8 members of this series is 224
This series corresponds to the following straight line y=2x+21
Finding the nthelement
a1 =a1+(n-1)*d =21+(1-1)*2 =21
a2 =a1+(n-1)*d =21+(2-1)*2 =23
a3 =a1+(n-1)*d =21+(3-1)*2 =25
a4 =a1+(n-1)*d =21+(4-1)*2 =27
a5 =a1+(n-1)*d =21+(5-1)*2 =29
a6 =a1+(n-1)*d =21+(6-1)*2 =31
a7 =a1+(n-1)*d =21+(7-1)*2 =33
a8 =a1+(n-1)*d =21+(8-1)*2 =35
a9 =a1+(n-1)*d =21+(9-1)*2 =37
a10 =a1+(n-1)*d =21+(10-1)*2 =39
a11 =a1+(n-1)*d =21+(11-1)*2 =41
a12 =a1+(n-1)*d =21+(12-1)*2 =43
a13 =a1+(n-1)*d =21+(13-1)*2 =45
a14 =a1+(n-1)*d =21+(14-1)*2 =47
a15 =a1+(n-1)*d =21+(15-1)*2 =49
a16 =a1+(n-1)*d =21+(16-1)*2 =51
a17 =a1+(n-1)*d =21+(17-1)*2 =53
a18 =a1+(n-1)*d =21+(18-1)*2 =55
a19 =a1+(n-1)*d =21+(19-1)*2 =57
a20 =a1+(n-1)*d =21+(20-1)*2 =59
a21 =a1+(n-1)*d =21+(21-1)*2 =61
a22 =a1+(n-1)*d =21+(22-1)*2 =63
a23 =a1+(n-1)*d =21+(23-1)*2 =65
a24 =a1+(n-1)*d =21+(24-1)*2 =67
a25 =a1+(n-1)*d =21+(25-1)*2 =69
a26 =a1+(n-1)*d =21+(26-1)*2 =71
a27 =a1+(n-1)*d =21+(27-1)*2 =73
a28 =a1+(n-1)*d =21+(28-1)*2 =75
a29 =a1+(n-1)*d =21+(29-1)*2 =77
a30 =a1+(n-1)*d =21+(30-1)*2 =79
a31 =a1+(n-1)*d =21+(31-1)*2 =81
a32 =a1+(n-1)*d =21+(32-1)*2 =83
a33 =a1+(n-1)*d =21+(33-1)*2 =85
Answer:
21,23,25,27,29,31,33,35
Your input 21,23,25,27,29,31,33,35 appears to be an arithmetic sequence
Find the difference between the members
a2-a1=23-21=2
a3-a2=25-23=2
a4-a3=27-25=2
a5-a4=29-27=2
a6-a5=31-29=2
a7-a6=33-31=2
a8-a7=35-33=2
The difference between every two adjacent members of the series is constant and equal to 2
General Form: an=a1+(n-1)d
an=21+(n-1)2
a1=21 (this is the 1st member)
an=35 (this is the last/nth member)
d=2 (this is the difference between consecutive members)
n=8 (this is the number of members)
Sum of finite series members
The sum of the members of a finite arithmetic progression is called an arithmetic series.
Using our example, consider the sum:
21+23+25+27+29+31+33+35
This sum can be found quickly by taking the number n of terms being added (here 8), multiplying by the sum of the first and last number in the progression (here 21 + 35 = 56), and dividing by 2:
n(a1+an)2
8(21+35)
2
The sum of the 8 members of this series is 224
This series corresponds to the following straight line y=2x+21
Finding the nthelement
a1 =a1+(n-1)*d =21+(1-1)*2 =21
a2 =a1+(n-1)*d =21+(2-1)*2 =23
a3 =a1+(n-1)*d =21+(3-1)*2 =25
a4 =a1+(n-1)*d =21+(4-1)*2 =27
a5 =a1+(n-1)*d =21+(5-1)*2 =29
a6 =a1+(n-1)*d =21+(6-1)*2 =31
a7 =a1+(n-1)*d =21+(7-1)*2 =33
a8 =a1+(n-1)*d =21+(8-1)*2 =35
a9 =a1+(n-1)*d =21+(9-1)*2 =37
a10 =a1+(n-1)*d =21+(10-1)*2 =39
a11 =a1+(n-1)*d =21+(11-1)*2 =41
a12 =a1+(n-1)*d =21+(12-1)*2 =43
a13 =a1+(n-1)*d =21+(13-1)*2 =45
a14 =a1+(n-1)*d =21+(14-1)*2 =47
a15 =a1+(n-1)*d =21+(15-1)*2 =49
a16 =a1+(n-1)*d =21+(16-1)*2 =51
a17 =a1+(n-1)*d =21+(17-1)*2 =53
a18 =a1+(n-1)*d =21+(18-1)*2 =55
a19 =a1+(n-1)*d =21+(19-1)*2 =57
a20 =a1+(n-1)*d =21+(20-1)*2 =59
a21 =a1+(n-1)*d =21+(21-1)*2 =61
a22 =a1+(n-1)*d =21+(22-1)*2 =63
a23 =a1+(n-1)*d =21+(23-1)*2 =65
a24 =a1+(n-1)*d =21+(24-1)*2 =67
a25 =a1+(n-1)*d =21+(25-1)*2 =69
a26 =a1+(n-1)*d =21+(26-1)*2 =71
a27 =a1+(n-1)*d =21+(27-1)*2 =73
a28 =a1+(n-1)*d =21+(28-1)*2 =75
a29 =a1+(n-1)*d =21+(29-1)*2 =77
a30 =a1+(n-1)*d =21+(30-1)*2 =79
a31 =a1+(n-1)*d =21+(31-1)*2 =81
a32 =a1+(n-1)*d =21+(32-1)*2 =83
a33 =a1+(n-1)*d =21+(33-1)*2 =85