Question

the arithmetic mean of the observation: 9,8,27,36 and 45 is​

Answer 1

a2-a1=18-9=9

a3-a2=27-18=9

a4-a3=36-27=9

a5-a4=45-36=9

The difference between every two adjacent members of the series is constant and equal to 9

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

an=9+(n-1)9

a1=9 (this is the 1st member)

an=45 (this is the last/nth member)

d=9 (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:

9+18+27+36+45

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 9 + 45 = 54), and dividing by 2:

n(a1+an)

2

5(9+45)

2

The sum of the 5 members of this series is 135

This series corresponds to the following straight line y=9x+9

Finding the nth element

a1 =a1+(n-1)*d =9+(1-1)*9 =9

a2 =a1+(n-1)*d =9+(2-1)*9 =18

a3 =a1+(n-1)*d =9+(3-1)*9 =27

a4 =a1+(n-1)*d =9+(4-1)*9 =36

a5 =a1+(n-1)*d =9+(5-1)*9 =45

a6 =a1+(n-1)*d =9+(6-1)*9 =54

a7 =a1+(n-1)*d =9+(7-1)*9 =63

a8 =a1+(n-1)*d =9+(8-1)*9 =72

a9 =a1+(n-1)*d =9+(9-1)*9 =81

a10 =a1+(n-1)*d =9+(10-1)*9 =90

a11 =a1+(n-1)*d =9+(11-1)*9 =99

a12 =a1+(n-1)*d =9+(12-1)*9 =108

a13 =a1+(n-1)*d =9+(13-1)*9 =117

a14 =a1+(n-1)*d =9+(14-1)*9 =126

a15 =a1+(n-1)*d =9+(15-1)*9 =135

a16 =a1+(n-1)*d =9+(16-1)*9 =144

a17 =a1+(n-1)*d =9+(17-1)*9 =153

a18 =a1+(n-1)*d =9+(18-1)*9 =162

a19 =a1+(n-1)*d =9+(19-1)*9 =171

a20 =a1+(n-1)*d =9+(20-1)*9 =180

a21 =a1+(n-1)*d =9+(21-1)*9 =189

a22 =a1+(n-1)*d =9+(22-1)*9 =198

a23 =a1+(n-1)*d =9+(23-1)*9 =207

a24 =a1+(n-1)*d =9+(24-1)*9 =216

a25 =a1+(n-1)*d =9+(25-1)*9 =225

a26 =a1+(n-1)*d =9+(26-1)*9 =234

a27 =a1+(n-1)*d =9+(27-1)*9 =243

a28 =a1+(n-1)*d =9+(28-1)*9 =252

a29 =a1+(n-1)*d =9+(29-1)*9 =261

a30 =a1+(n-1)*d =9+(30-1)*9 =270

Answer 2

The arithmetic mean of the observation is 25.

Explanation:

The numbers in a data set or observation are given as 9,8,27,36 and 45 and there are total of 5 numbers in the observation.We know,that the arithmetic mean or the average of the numbers within any data set or observation can be obtained by dividing the total sum or addition of all the individual numbers within the observation by the actual numbers present in the set or observation.

Hence,using the formula to find mean or average,the arithmetic mean in this case=$\frac{(9+8+27+36+45)}{5} =\frac{125}{5} =25$

Therefore,the arithmetic mean or average of the 5 numbers given in the question is 25.