Answer:
10,15,20,25,30,35,40,45
Your input 10,15,20,25,30,35,40,45 appears to be an arithmetic sequence
Find the difference between the members
a2-a1=15-10=5
a3-a2=20-15=5
a4-a3=25-20=5
a5-a4=30-25=5
a6-a5=35-30=5
a7-a6=40-35=5
a8-a7=45-40=5
The difference between every two adjacent members of the series is constant and equal to 5
General Form: an=a1+(n-1)d
an=10+(n-1)5
a1=10 (this is the 1st member)
an=45 (this is the last/nth member)
d=5 (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:
10+15+20+25+30+35+40+45
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 10 + 45 = 55), and dividing by 2:
n(a1+an)2
8(10+45)
2
The sum of the 8 members of this series is 220
This series corresponds to the following straight line y=5x+10
Finding the nthelement
a1 =a1+(n-1)*d =10+(1-1)*5 =10
a2 =a1+(n-1)*d =10+(2-1)*5 =15
a3 =a1+(n-1)*d =10+(3-1)*5 =20
a4 =a1+(n-1)*d =10+(4-1)*5 =25
a5 =a1+(n-1)*d =10+(5-1)*5 =30
a6 =a1+(n-1)*d =10+(6-1)*5 =35
a7 =a1+(n-1)*d =10+(7-1)*5 =40
a8 =a1+(n-1)*d =10+(8-1)*5 =45
a9 =a1+(n-1)*d =10+(9-1)*5 =50
