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Question

Use the given algebraic expression to complete the table of number patterns.

If the number of digits formed is taken to be n, the number of segments needed to form n digits is given by the algebraic expression appearing on the right of each pattern.

How many segments are needed to form 5,10,100 digits of the kind


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Solution

(a) From the given details we get to know that the numbers of segments needed to form n digits of the kind.
is (5n+1)

Then,

The number of segments needed to form 5 digits

=((5×5)+1)=(25+1)=26

The number of segments needed to form 10 digits

=((5×10)+1)=(50+1)=51

The number of segments needed to form 100 digits

=((5×100)+1)=(500+1)=501


(b) From the given details we get to know that the numbers of segments needed to form n digits of the kind
is (3n+1)

Then,

The number of segments needed to form 5digits

=((3×5)+1)=(15+1)=16

The number of segments needed to form 10 digits

=((3×10)+1)=(30+1)=31

The number of segments needed to form 100 digits

=((3×100)+1)=(300+1)=301

(c) From the given details we get to know that the numbers of segments needed to form n digits of the kind
is(5n+2)

Then,

The number of segments needed to form 5 digits

=((5×5)+2)=(25+2)=27

The number of segments needed to form 10 digits

=((5×10)+2)=(50+2)=52

The number of segments needed to form 100 digits

=((5×100)+2)=(500+2)=502

Hence, Number of segments that are needed to form 5,10,100 digits of the kind are 26,51,501.

Number of segments that are needed to form 5,10,100 digits of the kind are 16,31,301.

Number of segments that are needed to form 5,10,100 digits of the kind are 27,52,502.


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