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 $(5 n + 1)$
Then,
The number of segments needed to form $5$ digits
$= ((5 \times 5) + 1) = (25 + 1) = 26$
The number of segments needed to form $10$ digits
$= ((5 \times 10) + 1) = (50 + 1) = 51$
The number of segments needed to form $100$ digits
$= ((5 \times 100) + 1) = (500 + 1) = 501$

(b) From the given details we get to know that the numbers of segments needed to form $n$ digits of the kind
is $(3 n + 1)$
Then,
The number of segments needed to form $5$ digits
$= ((3 \times 5) + 1) = (15 + 1) = 16$
The number of segments needed to form 10 digits
$= ((3 \times 10) + 1) = (30 + 1) = 31$
The number of segments needed to form 100 digits
$= ((3 \times 100) + 1) = (300 + 1) = 301$
(c) From the given details we get to know that the numbers of segments needed to form $n$ digits of the kind
is $(5 n + 2)$
Then,
The number of segments needed to form $5$ digits
$= ((5 \times 5) + 2) = (25 + 2) = 27$
The number of segments needed to form 10 digits
$= ((5 \times 10) + 2) = (50 + 2) = 52$
The number of segments needed to form 100 digits
$= ((5 \times 100) + 2) = (500 + 2) = 502$
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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