Find the 29th term of the following sequence.
19.5, 19.9, 20.3, 20.7, . . .
Answers
Step-by-step explanation:
19.5,19.9,20.3,20.7
Your input 19.5,19.9,20.3,20.7 appears to be an arithmetic sequence
Find the difference between the members
a2-a1=19.9-19.5=0.4
a3-a2=20.3-19.9=0.4
a4-a3=20.7-20.3=0.4
The difference between every two adjacent members of the series is constant and equal to 0.4
General Form: an=a1+(n-1)d
an=19.5+(n-1)0.4
a1=19.5 (this is the 1st member)
an=20.7 (this is the last/nth member)
d=0.4 (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:
19.5+19.9+20.3+20.7
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 19.5 + 20.7 = 40.2), and dividing by 2:
n(a1+an)
2
4(19.5+20.7)
2
The sum of the 4 members of this series is 80.4
This series corresponds to the following straight line y=0.4x+19.5