Math, asked by priyapriyadars14, 1 month ago

complete the number pattern 13,23,33,43​

Answers

Answered by sakshi1158
3

Answer:

Your input 13,23,33,43,53,63,73,83 appears to be an arithmetic sequence

Find the difference between the members

a2-a1=23-13=10

a3-a2=33-23=10

a4-a3=43-33=10

a5-a4=53-43=10

a6-a5=63-53=10

a7-a6=73-63=10

a8-a7=83-73=10

The difference between every two adjacent members of the series is constant and equal to 10

General Form: a

n

=a

1

+(n-1)d

a

n

=13+(n-1)10

a1=13 (this is the 1st member)

an=83 (this is the last/nth member)

d=10 (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:

13+23+33+43+53+63+73+83

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 13 + 83 = 96), and dividing by 2:

n(a1+an)

2

8(13+83)

2

The sum of the 8 members of this series is 384

This series corresponds to the following straight line y=10x+13

Finding the n

th

element

a1 =a1+(n-1)*d =13+(1-1)*10 =13

a2 =a1+(n-1)*d =13+(2-1)*10 =23

a3 =a1+(n-1)*d =13+(3-1)*10 =33

a4 =a1+(n-1)*d =13+(4-1)*10 =43

a5 =a1+(n-1)*d =13+(5-1)*10 =53

a6 =a1+(n-1)*d =13+(6-1)*10 =63

a7 =a1+(n-1)*d =13+(7-1)*10 =73

a8 =a1+(n-1)*d =13+(8-1)*10 =83

a9 =a1+(n-1)*d =13+(9-1)*10 =93

a10 =a1+(n-1)*d =13+(10-1)*10 =103

a11 =a1+(n-1)*d =13+(11-1)*10 =113

a12 =a1+(n-1)*d =13+(12-1)*10 =123

a13 =a1+(n-1)*d =13+(13-1)*10 =133

a14 =a1+(n-1)*d =13+(14-1)*10 =143

a15 =a1+(n-1)*d =13+(15-1)*10 =153

a16 =a1+(n-1)*d =13+(16-1)*10 =163

a17 =a1+(n-1)*d =13+(17-1)*10 =173

a18 =a1+(n-1)*d =13+(18-1)*10 =183

a19 =a1+(n-1)*d =13+(19-1)*10 =193

a20 =a1+(n-1)*d =13+(20-1)*10 =203

a21 =a1+(n-1)*d =13+(21-1)*10 =213

a22 =a1+(n-1)*d =13+(22-1)*10 =223

a23 =a1+(n-1)*d =13+(23-1)*10 =233

a24 =a1+(n-1)*d =13+(24-1)*10 =243

a25 =a1+(n-1)*d =13+(25-1)*10 =253

a26 =a1+(n-1)*d =13+(26-1)*10 =263

a27 =a1+(n-1)*d =13+(27-1)*10 =273

a28 =a1+(n-1)*d =13+(28-1)*10 =283

a29 =a1+(n-1)*d =13+(29-1)*10 =293

a30 =a1+(n-1)*d =13+(30-1)*10 =303

a31 =a1+(n-1)*d =13+(31-1)*10 =313

a32 =a1+(n-1)*d =13+(32-1)*10 =323

a33 =a1+(n-1)*d =13+(33-1)*10 =333

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