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	1	17	-	-	-	-	-	-
iv	\[7n + 20\]	27	34	41	48	-	-	-	-	-	-
v	\[{n^2} + 1\]	2	5	10	17	-	-	-	-	10001	-

Answer 1

Hint: Substitute the term number in the given expression to find the values of the algebraic expression. Where algebraic expression is an expression built up from integer constants, variables and operators, we can derive the algebraic expression for a given condition by using +, -, ×, ÷.

Complete step-by-step answer:
Let the terms be n,
i.In the expression\[2n - 1\]
For the 100th term, n=100
\[
   = 2n - 1 \\
   = \left( {2 \times 100} \right) - 1 \\
   = 200 - 1 \\
   = 199 \\
 \]

ii.In the expression \[3n + 2\]
When n=5
\[
   = 3n + 2 \\
   = \left( {3 \times 5} \right) + 2 \\
   = 15 + 2 \\
   = 17 \\
 \]
When n=10
\[
   = 3n + 2 \\
   = \left( {3 \times 10} \right) + 2 \\
   = 30 + 2 \\
   = 32 \\
 \]
When n=100
\[
   = 3n + 2 \\
   = \left( {3 \times 100} \right) + 2 \\
   = 300 + 2 \\
   = 302 \\
 \]

iii.In the expression \[4n + 1\]
When n=5
\[
   = 4n + 1 \\
   = \left( {4 \times 5} \right) + 1 \\
   = 20 + 1 \\
   = 21 \\
 \]
When n=10
\[
   = 4n + 1 \\
   = \left( {4 \times 10} \right) + 1 \\
   = 40 + 1 \\
   = 41 \\
 \]
When n=100
\[
   = 4n + 1 \\
   = \left( {4 \times 100} \right) + 1 \\
   = 400 + 1 \\
   = 401 \\
 \]

In the expression \[7n + 20\]
When n=5
\[
   = 7n + 20 \\
iv. = \left( {7 \times 5} \right) + 20 \\
   = 35 + 20 \\
   = 55 \\
 \]
When n=10
\[
   = 7n + 20 \\
   = \left( {7 \times 10} \right) + 20 \\
   = 70 + 20 \\
   = 90 \\
 \]
When n=100

\[
   = 7n + 20 \\
   = \left( {7 \times 100} \right) + 20 \\
   = 700 + 20 \\
   = 720 \\
 \]

v.In the expression \[{n^2} + 1\]
When n=5
\[
   = {n^2} + 1 \\
   = {5^2} + 1 \\
   = 25 + 1 \\
   = 26 \\
 \]
When n=10
\[
   = {n^2} + 1 \\
   = {10^2} + 1 \\
   = 100 + 1 \\
   = 101 \\
 \]
  Now put all the value of the expression for n in the given table

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	1	17	21	-	41	-	401	-
iv	\[7n + 20\]	27	34	41	48	55	-	90	-	720	-
v	\[{n^2} + 1\]	2	5	10	17	26	-	101	-	10001	-

Note: Students should be careful while filling the data in the table. Each data should be filled only corresponding to the row and column only. Be careful and take all n values required as per the question.