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Question 2
Use the given algebraic expression to complete the table of number patterns:
TermsS.NoExpression1st2nd3rd4th5th...10th...100th...(i)2n11357919(ii)3n+225811(iii)4n+1591317(iv)7n+2027344148(v)n2+125101710001

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Solution

(i) 2n-1

Putting n = 10, 2×101=201=19
Putting n = 100, 2×1001=2001=199

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

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

(iv) 7n+20
Putting n = 5, 7×5+20=25+20=55
Putting n = 10, 7×10+20=70+20=90
Putting n = 100, 7×100+20=700+20=720

(v) n2+1
Putting n = 5, 5×5+1=25+1=26
Putting n = 10, 10×10+1=100+1=101
Putting n = 100, 100×100+1=10000+1=10001
Now complete table is,
TermsS.NoExpression1st2nd3rd4th5th...10th...100th...(i)2n11357919199(ii)3n+2258111732302(iii)4n+15913172141401(iv)7n+20273441485590720(v)n2+12510172610110001


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