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Question -

Use the given algebraic expression to complete the table of number patterns:

S.No.

Expression

Terms

1st

2nd

3rd

4th

5th

…

10th

…

100th

…

(i)

2n – 1

1

3

5

7

9

–

19

–

–

–

(ii)

3n + 2

5

8

11

14

–

–

–

–

–

–

(iii)

4n + 1

5

9

13

17

–

–

–

–

–

–

(iv)

7n + 20

27

34

41

48

–

–

–

–

–

–

(v)

n2 + 1

2

5

10

17

–

–

–

–

10,001

–



Answer -

(i) Given expressionis 2n – 1
For n = 100, 2 × 100 – 1
= 200 – 1 = 199

(ii) Given expressionis 3n + 2
For n = 5, 3 × 5 + 2 = 15 + 2 = 17
For n = 10, 3 × 10 + 2 = 30 + 2 = 32
For n = 100, 3 × 100 + 2 = 300 + 2 = 302

(iii) Given expressionis 4n + 1
For n = 5, 4 × 5 + 1 = 20 + 1 = 21
For n = 10, 4 × 10 + 1 = 40 + 1 = 41
For n = 100, 4 × 100 + 1 = 400 + 1 = 401

(iv) Given expressionis 7n + 20
For n = 5, 7 × 5 + 20 = 35 + 20 = 55
For n = 10, 7 × 10 + 20 = 70 + 20 = 90
For n = 100, 7 × 100 + 20 = 700 + 20 = 720

(v) Given expressionis n2 + 1
For n = 5, 52 + 1 = 25 + 1 = 26
For n = 10, 102 + 1 = 100 + 1 = 101

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