Ex 12.4 Q2 Algebraic Expressions Solution - NCERT Maths Class 7

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Question

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

S. No.

Expression

Terms

1st

2nd

3rd

4th

5th

...

10th

100th

(i)

\(2n – 1\)

\(1\)

\(3\)

\(5\)

\(7\)

\(9\)

-

\(19\)

-

-

-

(ii)

\(3n+2\)

\(5\)

\(8\)

\(11\)

\(14\)

-

-

-

-

-

-

(iii)

\(4n + 1\)

\(5\)

\(9\)

\(13\)

\(17\)

-

-

-

-

-

-

(iv)

\(7n + 20\)

\(27\)

\(34\)

\(41\)

\(48\)

-

-

-

-

-

-

(v)

\(n^2 +1\)

\(2\)

\(5\)

\(10\)

\(17\)

-

-

-

-

\(10,001\)

-

Text Solution

What is known?

Different algebraic expressions and the terms.

What is unknown?

Some terms of the given algebraic expression.

Reasoning:

This question is very simple put the value of n in the given algebraic expression and you can easily find out the unknown terms.

Steps:

Putting value of \(n = 5, 10\) and \(100\)

(i) \(2n – 1\)

\[\begin{align}2 \times 100 - 1 & = 200 - 1\\& = 199\end{align}\]

(ii) \(3n+2\)

\[\begin{align}3 \times 5 + 2 & = 15 + 2\\ & = 17\\\ 3 \times 10 + 2&=30+ 2\\ &= 32 \\ 3 \times 100 + 2 & = 300 + 2\\& = 302\\\end{align}\]

(iii) \(4n+1\)

\[\begin{align}4 \times 5 + 1& = 20 + 1\\&= 21\\  4 \times 10 + 1&= 40 + 1\\ &  = 41\\4 \times 100 + 1&= 400 + 1\\ & = 401\end{align}\]

(iv) \(7n+2\)

\[\begin{align}7 \times 5 + 20 & = 35 + 20\\&= 55\\7 \times 10 + 20 & = 70 + 20\\&= 90\\7 \times 100 + 20  & = 700 + 20\\&= 720\end{align}\]

(v) \(n^2+1\)

\[\begin{align}5 \times 5 + 1 & = 25 + 1\\& = 26\\10 \times 10 + 1 & = 100 + 1\\& = 101\\100 \times 100 + 1 & = 10000 + 1\\&  = 10001\end{align}\]

Complete table is:

S.No.

Expression

Terms

1st

2nd

3rd

4th

5th

...

10th

100th

(i)

\(2n – 1\)

\(1\)

\(3\)

\(5\)

\(7\)

\(9\)

-

\(19\)

-

\(199\)

-

(ii)

\(3n + 2\)

\(5\)

\(8\)

\(11\)

\(14\)

\(17\)

-

\(32\)

-

\(302\)

-

(iii)

\(4n + 1\)

\(5\)

\(9\)

\(13\)

\(17\)

\(21\)

-

\(41\)

-

\(401\)

-

(iv)

\(7n + 20\)

\(27\)

\(34\)

\(41\)

\(48\)

\(55\)

-

\(90\)

-

\(720\)

-

(v)

\(n^2 + 1\)

\(2\)

\(5\)

\(10\)

\(17\)

\(26\)

-

\(101\)

-

\(10,001\)

-

  
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