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 digits of the kind

For digit

Expression : 5n + 1

Where n = no of digits

For 5 digits

No of segments required = 5(5) + 1 = 25 + 1 = 26

For 10 digits

No of segments required = 5(10) + 1 = 50 + 1 = 51

For 100 digits

No of segments required = 5(100) + 1 = 500 + 1 = 501

For digit

Expression : 3n + 1

Where n = no of digits

For 5 digits

No of segments required = 3(5) + 1 = 15 + 1 = 16

For 10 digits

No of segments required = 3(10) + 1 = 30 + 1 = 31

For 100 digits

No of segments required = 3(100) + 1 = 300 + 1 = 301

For digit

Expression : 5n + 2

Where n = no of digits

For 5 digits

No of segments required = 5(5) + 2 = 25 + 2 = 27

For 10 digits

No of segments required = 5(10) + 2 = 50 + 2 = 52

For 100 digits

No of segments required = 5(100) + 2 = 500 + 2 = 502