Question

Question 2
Use the given algebraic expression to complete the table of number patterns:
$\begin{array}{cccccccccccc}& & & & Terms& & & & & & & \\ S.No& Expression& 1^{st}& 2^{nd}& 3^{rd}& 4^{th}& 5^{th}& ...& {10}^{th}& ...& {100}^{th}& ...\\ \left(i\right)& 2n-1& 1& 3& 5& 7& 9& ---& 19& ---& ---& ---\\ \left(ii\right)& 3n+2& 2& 5& 8& 11& ---& ---& ---& ---& ---& ---\\ \left(iii\right)& 4n+1& 5& 9& 13& 17& ---& ---& ---& ---& ---& ---\\ \left(iv\right)& 7n+20& 27& 34& 41& 48& ---& ---& ---& ---& ---& ---\\ \left(v\right)& n^2+1& 2& 5& 10& 17& ---& ---& ---& ---& 10001& ---\end{array}$

Answer 1

(i) 2n-1

Putting n = 10, $2\times 10–1=20–1=19$
Putting n = 100, $2\times 100–1=200–1=199$

(ii) 3n + 2
Putting n = 5, $3\times 5+2=15+2=17$
Putting n = 10, $3\times 10+2=30+2=32$
Putting n = 100, $3\times 100+2=300+2=302$

(iii) 4n +1
Putting n = 5, $4\times 5+1=20+1=21$
Putting n = 10, $4\times 10+1=40+1=41$
Putting n = 100, $4\times 100+1=400+1=401$

(iv) 7n+20
Putting n = 5, $7\times 5+20=25+20=55$
Putting n = 10, $7\times 10+20=70+20=90$
Putting n = 100, $7\times 100+20=700+20=720$

(v) $n^2+1$
Putting n = 5, $5\times 5+1=25+1=26$
Putting n = 10, $10\times 10+1=100+1=101$
Putting n = 100, $100\times 100+1=10000+1=10001$
Now complete table is,
$\begin{array}{cccccccccccc}& & & & Terms& & & & & & & \\ S.No& Expression& 1^{st}& 2^{nd}& 3^{rd}& 4^{th}& 5^{th}& ...& {10}^{th}& ...& {100}^{th}& ...\\ \left(i\right)& 2n-1& 1& 3& 5& 7& 9& ---& 19& ---& 199& ---\\ \left(ii\right)& 3n+2& 2& 5& 8& 11& 17& ---& 32& ---& 302& ---\\ \left(iii\right)& 4n+1& 5& 9& 13& 17& 21& ---& 41& ---& 401& ---\\ \left(iv\right)& 7n+20& 27& 34& 41& 48& 55& ---& 90& ---& 720& ---\\ \left(v\right)& n^2+1& 2& 5& 10& 17& 26& ---& 101& ---& 10001& ---\end{array}$