question_answer 1)

Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators. (a) (b) (c) If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digit of the kind

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 \[=\text{5}\times \text{1}00+\text{2}=\text{5}00+\text{2}=\text{5}0\text{2}\].