Answer:
(a) Let the number of digits formed be n, Then, the number of segments required to form n digits is given by the algebraic expression \[5n+1\]. So, (i) the number of segments required to form 5 digits of the kind \[=5\times 5+1=25+1=26\] (ii) the number of segments required to form 10 digits of this kind \[=5\times 10+1=50+1=51\] (iii) the number of segment required to form 100 digits of this kind \[=5\times 100+1=500+1=501\] (b) Let the number of digits formed be n. Then, the number of segments required to form n digits is given by the algebraic expression \[3n+1\]. So, (i) the number of segments required to form 5 digits of this kind \[=3\times 5+1=15+1=16\] (ii) the number of segments required to form 10 digits of this kind \[=\text{3}\times \text{1}0+\text{1}=\text{3}0+\text{1}=\text{31}\] (iii) The number of segments required to form 100 digits of this kind \[=\text{3}\times \text{1}00+\text{1}=\text{3}00+\text{1}=\text{3}0\text{1}.\] (c) Let the number of digits formed be n. Then, the number of segments required to form n digits is given by the algebraic expression \[\text{5n}+\text{2}\]. So, (i) the number of segments required to form 5 digits of this kind \[=\text{5}\times \text{5}+\text{2}=\text{25}+\text{2}=\text{27}\] (ii) the number of segments required to form 10 digits of this kind \[=\text{5}\times \text{1}0+\text{2}=\text{5}0+\text{2}=\text{52}\] (iii) the number of segments required to form 100 digits of this kind \[=\text{5}\times \text{1}00+\text{2}=\text{5}00+\text{2}=\text{5}0\text{2}\].
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