Which sequence shall be obtained if we start adding the terms of the sequence of odd numbers?
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Expert Answer
Which sequence shall be obtained if we start adding the terms of the sequence of odd numbers?
Question 1.
Which sequence shall be obtained if we start adding the terms of the sequence of odd numbers?
Solution:
On adding the terms, we get (1 + 3), (1 + 3 + 5), (1 + 3 + 5 + 7), ...
Thus, we obtained the sequence of square numbers 1, 4, 9, 16, ...
Question 2.
What shall be obtained if we start adding the terms of the sequence of hexagonal numbers?
Solution:
On adding the terms, we get 1, 1 + 7, 1 + 7 + 19, 1 + 7 + 19 + 37, ...
Thus, we obtained the sequence of cube numbers 1, 8, 27, 64, ...
Question 3.
What is value of 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1?
Solution:
It is the case when terms of the sequence of counting numbers are added up and down.
So, the required value = 6 × 6 = 36.