Can you write t5, t6 t7 and t8 for the sequence of triangular numbers? Class 9
Can you write t5, t6 t7 and t8 for the sequence of triangular numbers? Class 9
Question 1.
Can you write t5, t6 t7 and t8 for the sequence of triangular numbers? Class 9
Answer:
Sequence of triangular numbers is 1, 3, 6,10 ...
t5 = 1 + 2 + 3 + 4 + 5 = 15,
t6 = 1 + 2 + 3 + 4 + 5 + 6 = 21,
t7 = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28,
t8 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.
Question 2.
Can you think of any other kinds of sequences? List out five different types of sequences and discuss their properties with your friends. Class 9
Answer:
Yes, different kinds of sequences can be seen in everyday life. Some examples are:
i. Dates on a calendar: 1, 2, 3, 4, 5, ... Property: Each number increases by 1.
ii. Even house numbers on a street: 2, 4, 6, 8, 10, ...
Property: Each term increases by 2.
iii. Countdown before a game starts: 10, 9, 8, 7, 6, ...
Property: Each term decreases by 1.
iv. Traffic signal pattern: Red, Yellow, Green, Red, Yellow, Green, ...
The days of the week follows a repeating Property: The pattern repeats in the same order.
v. Days of the week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, Monday, Tuesday, ...
Property: The terms repeat in a fixed order after every seven days.
[Note: Students may explore different patterns from everyday life, discuss their observations with friends, and frame their own answers.]