10 20 30 ....40...whats next
Answers
Question:
10 20 30 ....40...whats next?
Answer :
10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 and so on .
Explained method :
The given sequence is 10, 20, 30, 40, ...
First term = 10
Second term = 20
Third term = 30
...
We clearly see that the common difference between the first term and the second term is (20 - 10) = 10 and that of the second term and the third term is (30 - 20) = 10, and so on. We conclude that the sequence is in Arithmetic Progression.
Its n - th term be
= first term + (n - 1) (common difference)
= 10 + (n - 1) × 10
= 10 + 10n - 10
= 10n, which is a multiple of 10 where n belongs to the set of Natural Numbers.
Hence, the complete sequence be
10, 20, 30, 40, 50, ..., 10n, ...
Where n = Natural Number (N)
10, 20, 30, 40, 50, 60, 70 and so on
Step-by-step explanation:
The given sequence is 10, 20, 30, 40, ...
Here, 20 - 10 = 10, 30 - 20 = 10, 40 - 30 = 10 and thus we can conclude that the given sequence is an Arithmetic Progression whose first term is 10 and the common difference is 10.
Thus the terms that come after 40 are
- 40 + 10 = 50,
- 50 + 10 = 60,
- 60 + 10 = 70 and so on.
Note 1.
However we can use the formula for n-th term:
n-th term = a + (n - 1)d, where a is the first term of the progression and d the common difference.
Note 2.
We can also see that the sequence 10, 20, 30, 40, ... contains the multiples of 10.
So, the next terms are 50, 60, 70 and so on.