Question

common difference of the arthimetic progression 1.5,3,4.5,6......is​

Answer 1

Answer:

Hope this helps you

Step-by-step explanation:

Your input 1.5,3,4.5,6,7.5 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

a5-a4=7.5-6=1.5

The difference between every two adjacent members of the series is constant and equal to 1.5

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

an=1.5+(n-1)1.5

a1=1.5   (this is the 1st member)

an=7.5  (this is the last/nth member)

d=1.5  (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:

1.5+3+4.5+6+7.5

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 1.5 + 7.5 = 9), and dividing by 2:

n(a1+an)2

5(1.5+7.5)

     2

The sum of the 5 members of this series is 22.5

This series corresponds to the following straight line y=1.5x+1.5

Finding the nthelement

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

a30 =a1+(n-1)*d =1.5+(30-1)*1.5 =45

Answer 2

Answer:

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