Question

2,6,10,14....... is the sum an arithmetic progression

Answer 1

Find the difference between the members

a2-a1=6-2=4a3-a2=10-6=4a4-a3=14-10=4a5-a4=18-14=4

The difference between every two adjacent members of the series is constant and equal to 4

General Form: an=a1+(n-1)d

an=2+(n-1)4

a1=2   (this is the 1st member)
an=18  (this is the last/nth member)
d=4  (this is the difference between consecutive members)
n=5  (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:

2+6+10+14+18

This sum can be found quickly by taking the number n of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 2 + 18 = 20), and dividing by 2:

n(a1+an)2
5(2+18)
     2

The sum of the 5 members of this series is 50

This

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Answer 2

Hey frnd,
here is ur answer
2,6,10,14 =sum of an observation
and 4 = Total no.of an observation
so
M=sum of an observation
-----------------------------------------
total no.of an observation

M=2+6+10+14
----------------
4
M= 32
------
4
M=8 is ur answer
Hope it helps.