Question

what is the 20th term of arithematic sequence1, 18,15​

Answer 1

Step-by-step explanation:

1,8,15,22,29,36,43,50

Your input 1,8,15,22,29,36,43,50 appears to be an arithmetic sequence

Find the difference between the members

a2-a1=8-1=7

a3-a2=15-8=7

a4-a3=22-15=7

a5-a4=29-22=7

a6-a5=36-29=7

a7-a6=43-36=7

a8-a7=50-43=7

The difference between every two adjacent members of the series is constant and equal to 7

General Form: a

n

=a

1

+(n-1)d

a

n

=1+(n-1)7

a1=1 (this is the 1st member)

an=50 (this is the last/nth member)

d=7 (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:

1+8+15+22+29+36+43+50

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 1 + 50 = 51), and dividing by 2:

n(a1+an)

2

8(1+50)

2

The sum of the 8 members of this series is 204

This series corresponds to the following straight line y=7x+1

Finding the n

th

element

a1 =a1+(n-1)*d =1+(1-1)*7 =1

a2 =a1+(n-1)*d =1+(2-1)*7 =8

a3 =a1+(n-1)*d =1+(3-1)*7 =15

a4 =a1+(n-1)*d =1+(4-1)*7 =22

a5 =a1+(n-1)*d =1+(5-1)*7 =29

a6 =a1+(n-1)*d =1+(6-1)*7 =36

a7 =a1+(n-1)*d =1+(7-1)*7 =43

a8 =a1+(n-1)*d =1+(8-1)*7 =50

a9 =a1+(n-1)*d =1+(9-1)*7 =57

a10 =a1+(n-1)*d =1+(10-1)*7 =64

a11 =a1+(n-1)*d =1+(11-1)*7 =71

a12 =a1+(n-1)*d =1+(12-1)*7 =78

a13 =a1+(n-1)*d =1+(13-1)*7 =85

a14 =a1+(n-1)*d =1+(14-1)*7 =92

a15 =a1+(n-1)*d =1+(15-1)*7 =99

a16 =a1+(n-1)*d =1+(16-1)*7 =106

a17 =a1+(n-1)*d =1+(17-1)*7 =113

a18 =a1+(n-1)*d =1+(18-1)*7 =120

a19 =a1+(n-1)*d =1+(19-1)*7 =127

a20 =a1+(n-1)*d =1+(20-1)*7 =134

a21 =a1+(n-1)*d =1+(21-1)*7 =141

a22 =a1+(n-1)*d =1+(22-1)*7 =148

a23 =a1+(n-1)*d =1+(23-1)*7 =155

a24 =a1+(n-1)*d =1+(24-1)*7 =162

a25 =a1+(n-1)*d =1+(25-1)*7 =169

a26 =a1+(n-1)*d =1+(26-1)*7 =176

a27 =a1+(n-1)*d =1+(27-1)*7 =183

a28 =a1+(n-1)*d =1+(28-1)*7 =190

a29 =a1+(n-1)*d =1+(29-1)*7 =197

a30 =a1+(n-1)*d =1+(30-1)*7 =204

a31 =a1+(n-1)*d =1+(31-1)*7 =211

a32 =a1+(n-1)*d =1+(32-1)*7 =218

a33 =a1+(n-1)*d =1+(33-1)*7 =225