Question 13 Marks
Which number sequence is formed by counting the number of lines in each shape in the sequence of complete graphs?
Answer
View full question & answer→Sequence of triangular numbers i.e. $1,3,6,10,15,21, ....$
Questions
3 Marks Question
Take a timed test
8 questions · self-marked practice — reveal the answer and mark yourself.
Question 23 Marks
Explain why do you get the same number sequence in question 1 and question 2 ?
Answer
View full question & answer→self
Question 33 Marks
Which number sequence is formed by the number of corners in each shape in the sequence of regular polygons?
Answer
View full question & answer→3, 4, 5, 6, 7, 8, 9, 10, .....
Question 43 Marks
Which number sequence is formed by the number of sides in each shape in the sequence of regular polygons?
Answer
View full question & answer→3, 4, 5, 6, 7, 8, 9, 10, .....
Question 53 Marks
Using the pattern discussed on page 1.11, find the value of
$1+2+3+....+99+100+99+....+3+2+1$
$1+2+3+....+99+100+99+....+3+2+1$
Answer
View full question & answer→10000
Question 63 Marks
Study the following pattern:
$
\begin{array}{ll}
1 & =\frac{1 \times 2}{2} \\
1+2 & =\frac{2 \times 3}{2} \\
1+2+3 & =\frac{3 \times 4}{2} \\
1+2+3+4 & =\frac{4 \times 5}{2}
\end{array}
$
By observing the above pattern, find:
(i) $1+2+3+4+5+6+7+8+9+10$
(ii) $50+51+52+......+100$
(iii) $2+4+6+8+10+......+100$
$
\begin{array}{ll}
1 & =\frac{1 \times 2}{2} \\
1+2 & =\frac{2 \times 3}{2} \\
1+2+3 & =\frac{3 \times 4}{2} \\
1+2+3+4 & =\frac{4 \times 5}{2}
\end{array}
$
By observing the above pattern, find:
(i) $1+2+3+4+5+6+7+8+9+10$
(ii) $50+51+52+......+100$
(iii) $2+4+6+8+10+......+100$
Answer
View full question & answer→(i) $\frac{10 \times 11}{2}=55$
(ii) $\frac{100 \times 101}{2}-\frac{49 \times 50}{2}=3825$
(iii) $2\left(\frac{50 \times 51}{2}\right)=2550$
(ii) $\frac{100 \times 101}{2}-\frac{49 \times 50}{2}=3825$
(iii) $2\left(\frac{50 \times 51}{2}\right)=2550$
Question 73 Marks
Study the following pattern:
$
\begin{array}{ll}
1+3 & =2 \times 2 \\
1+3+5 & =3 \times 3 \\
1+3+5+7 & =4 \times 4 \\
1+3+5+7+9 & =5 \times 5
\end{array}
$
By ohserving the above pattern, find:
(i) $...+3+5+7+9+11$
(ii) $1+3+5+7+9+11+13+15$
(iii) $21+23+25+\ldots \ldots+51$
$
\begin{array}{ll}
1+3 & =2 \times 2 \\
1+3+5 & =3 \times 3 \\
1+3+5+7 & =4 \times 4 \\
1+3+5+7+9 & =5 \times 5
\end{array}
$
By ohserving the above pattern, find:
(i) $...+3+5+7+9+11$
(ii) $1+3+5+7+9+11+13+15$
(iii) $21+23+25+\ldots \ldots+51$
Answer
View full question & answer→(i) $6 \times 6=36$
(ii) $8 \times 8=64$
(iii) $26 \times 26-10 \times 10$
(ii) $8 \times 8=64$
(iii) $26 \times 26-10 \times 10$
Question 83 Marks
Observe the following pattern and extend it to three more steps:
Answer
$\begin{array}{l}10 \times 6-45=15 \\ 11 \times 7-60=17 \\ 12 \times 8-77=19\end{array}$
View full question & answer→$\begin{array}{l}10 \times 6-45=15 \\ 11 \times 7-60=17 \\ 12 \times 8-77=19\end{array}$