Writing Number Patterns and Rules Related to Them

Q. The $n^{th}$ term of the pattern 0, 3, 8, 15, 24...... is _____.

1. $n-1$
2. $n^2-1$
3. $n(n-1)$
4. $(n-1)(n-2)$

Q.

Set up an equation in the following cases:

(i) Irfan says that he has $7$ marbles more than five times the marbles Parmit has. Irfan has $37$ marbles. (Take $m$ to be the number of Parmit’s marbles.)

(ii) Laxmi’s father is $49$ years old. He is $4$ years older than three times Laxmi’s age. (Take Laxmi’s age to be $y$ years.)

(iii) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus $7$. The highest score is $87$. (Take the lowest score to be $l$.)

(iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be $b$ in degrees. Remember that the sum of angles of a triangle is $180$ degrees.)

Q.

The $n^{th}$ term of the pattern 1, 4, 9, 16, 25...... is _____.

1. n(n-1)

2. n+3

3. n+5

4. $n^2$

Q. In the following figures, polygons are formed by increasing the number of sides using matchsticks as given below.
Find the number of sticks required to form the next shape by tabulation and generalisation.

1. 9
2. 8
3. 12
4. 10

Q. This term is given as one of the alternatives given below each question. Find out this term. ASTN : ZTSO : : UIOZ : ?

1. LTTC
2. LRRC
3. TJNA
4. NTVC

Q.

Find the successor of $\left|-5^2-7^2\right|$

Q.

Question 4
Starting from (−1) $\times$ 5 , write various products showing a pattern to show (−1) $\times$ (−1)=1.

Q. Choose the correct pair of statements from the given ones.

1. 30 mins
2. 
3. 
4. 
5. 40 mins
6. 150 mins

Q.

If there is no sign before a term , it means ___________.

Q. How can we obtain Fibonacci sequence in the Pascal's Triangle?

Q. Construct a $3\times 3$ magic square to get a magic sum of $27$

Q. $T_m$ denotes the number of Triangles that can be formed with the vertices of a regular polygon of $m$ sides. If $T_{m+1}-T_m=15$ then $m=$

1. $6$
2. $12$
3. $9$
4. $3$

Q. Find the values of $(4.9{)}^2$

Q. The number of matchsticks required to make the given pattern can be given by $4n+1.$

1. False
2. True

Q.

Given Sara’s present age today is y years. Think of her age in the future or in the past. What will the following expression indicate?

$y+7,y-3,y+4\frac{1}{2},y-2\frac{1}{2}$

Q. Subtract the second expression from the first:
(iii) 5𝑎+𝑏, −6𝑏+2𝑎

Q. The number of matchsticks required to make the given pattern can be given by (5n + 1).

1. False
2. True

Q. The number of matchsticks required to make the given pattern can be given by $4n+1.$

1. False
2. True

Q.

Given below is a pattern made using squares. Observe the pattern and tell the number of squares in the next figure in the sequence. Also find the general form which represents the number of squares in the sequence.

1. The pattern doesn’t follow with the next set of squares

2. $25,n^2$

3. $16,n^2$

4. $25,2n+1$

Q. If all possible diagonals from a vertex of an 'n' sided polygon be drawn, then the number of triangles thus formed is

1. $n+1$
2. n
3. $n-1$
4. $n-2$

Q. If $y=a+\frac{b}{x}$, where $a$ and $b$ are constants and if $y=1$ when $x=-1$, and $y=5$ when $x=-5$, what is the value of $a+b$?

1. $-1$
2. $0$
3. $1$
4. $11$

Q. What is the quotient when $34ab$ is divided by $17a$ ?

1. $2$ a
2. $2$ b
3. $578a^{2}b$
4. $17b$

Q. Subtract the second expression from the first
(ii) −2𝑏+2𝑐, 𝑏+3𝑐

Q. You have a certain number of chocolates and you don't know the number of chocolates. If you receive the same number of chocolates from your friend, which of the following can represent the total number of chocolates you have?

1. $x^2$
2. $x+xy$ (Both x and y are different variables)
3. $x+y$ (Both x and y are different variables)
4. $2x$

Q. The number of matchsticks required to make the given pattern can be given by $4n+1.$

1. False
2. True

Q.

$5+(-3)-(-8)\mathrm{is}\mathrm{positve}$

1. True
2. False

Q.

If the sum of first $p,q,r$ terms of an A.P are $a,b,c$ respectively. Show that $\frac{a}{p}(q-r)+\frac{b}{q}(r-p)+\frac{c}{r}(p-q)=0$.

Q. How do you solve the inequality $32.4\ge -6c$?

Q.

$\left|-9\right|>6$

1. True
2. False

Q. The number of matchsticks required to make the given pattern can be given by (5n + 1).

1. False
2. True