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Question

# Question 2 Use the given algebraic expression to complete the table of number patterns: TermsS.NoExpression1st2nd3rd4th5th...10th...100th...(i)2n−113579−−−19−−−−−−−−−(ii)3n+225811−−−−−−−−−−−−−−−−−−(iii)4n+1591317−−−−−−−−−−−−−−−−−−(iv)7n+2027344148−−−−−−−−−−−−−−−−−−(v)n2+1251017−−−−−−−−−−−−10001−−−

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Solution

## (i) 2n-1 Putting n = 10, 2×10–1=20–1=19 Putting n = 100, 2×100–1=200–1=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)2n−113579−−−19−−−199−−−(ii)3n+22581117−−−32−−−302−−−(iii)4n+159131721−−−41−−−401−−−(iv)7n+202734414855−−−90−−−720−−−(v)n2+125101726−−−101−−−10001−−−

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