1.5,3,4.5,6
Your input 1.5,3,4.5,6 appears to be an arithmetic sequence
Find the difference between the members
a2-a1=3-1.5=1.5
a3-a2=4.5-3=1.5
a4-a3=6-4.5=1.5
The difference between every two adjacent members of the series is constant and equal to 1.5
General Form: a
n
=a
1
+(n-1)d
a
n
=1.5+(n-1)1.5
a1=1.5 (this is the 1st member)
an=6 (this is the last/nth member)
d=1.5 (this is the difference between consecutive members)
n=4 (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:
1.5+3+4.5+6
This sum can be found quickly by taking the number n of terms being added (here 4), multiplying by the sum of the first and last number in the progression (here 1.5 + 6 = 7.5), and dividing by 2:
n(a1+an)
2
4(1.5+6)
2
The sum of the 4 members of this series is 15
This series corresponds to the following straight line y=1.5x+1.5
Finding the n
th
element
a1 =a1+(n-1)*d =1.5+(1-1)*1.5 =1.5
a2 =a1+(n-1)*d =1.5+(2-1)*1.5 =3
a3 =a1+(n-1)*d =1.5+(3-1)*1.5 =4.5
a4 =a1+(n-1)*d =1.5+(4-1)*1.5 =6
a5 =a1+(n-1)*d =1.5+(5-1)*1.5 =7.5
a6 =a1+(n-1)*d =1.5+(6-1)*1.5 =9
a7 =a1+(n-1)*d =1.5+(7-1)*1.5 =10.5
a8 =a1+(n-1)*d =1.5+(8-1)*1.5 =12
a9 =a1+(n-1)*d =1.5+(9-1)*1.5 =13.5
a10 =a1+(n-1)*d =1.5+(10-1)*1.5 =15
a11 =a1+(n-1)*d =1.5+(11-1)*1.5 =16.5
a12 =a1+(n-1)*d =1.5+(12-1)*1.5 =18
a13 =a1+(n-1)*d =1.5+(13-1)*1.5 =19.5
a14 =a1+(n-1)*d =1.5+(14-1)*1.5 =21
a15 =a1+(n-1)*d =1.5+(15-1)*1.5 =22.5
a16 =a1+(n-1)*d =1.5+(16-1)*1.5 =24
a17 =a1+(n-1)*d =1.5+(17-1)*1.5 =25.5
a18 =a1+(n-1)*d =1.5+(18-1)*1.5 =27
a19 =a1+(n-1)*d =1.5+(19-1)*1.5 =28.5
a20 =a1+(n-1)*d =1.5+(20-1)*1.5 =30
a21 =a1+(n-1)*d =1.5+(21-1)*1.5 =31.5
a22 =a1+(n-1)*d =1.5+(22-1)*1.5 =33
a23 =a1+(n-1)*d =1.5+(23-1)*1.5 =34.5
a24 =a1+(n-1)*d =1.5+(24-1)*1.5 =36
a25 =a1+(n-1)*d =1.5+(25-1)*1.5 =37.5
a26 =a1+(n-1)*d =1.5+(26-1)*1.5 =39
a27 =a1+(n-1)*d =1.5+(27-1)*1.5 =40.5
a28 =a1+(n-1)*d =1.5+(28-1)*1.5 =42
a29 =a1+(n-1)*d =1.5+(29-1)*1.5 =43.5
