1,6,11,16....is the sequence in which 1 or 6 comes in the right end of the number which number is added repeatedly to get the terms of the sequence
Answers
Step-by-step explanation:
Given data :
Sequence = 1,6, 11, 16,... In which 1 or 6 comes in the right end of the Number.
To find :
Next five terms in the sequence.
Largest 2 digit term in the sequence.
No.of numbers in this sequence which are below 100 by actual counting.
Count without actual counting.
Step by step explanation :
1) Next five terms in the sequence.
The series is going with alternate endings of 1 and 6. So, all we need to do is to go with next nearest number that ends with 1 and then with the number that ends with 5 and the same thing repeats on.
The next 5 terms in the sequence are 1, 6, 11, 16, 21, 26, 31, 36, 41, ....
2) Largest 2 digit term in the sequence.
The series goes on with the numbers that ends with 1 and then 6. Below 100, the last two numbers that ends with 1 and 6 are 91 and 96. So,
Largest 2 digit term in the sequence is 96.
3) No.of numbers in this sequence which are below 100 by actual counting.
As the series is going with alternate endings of 1 and 6. So, all we need to do is to go with next nearest number that ends with 1 and then with the number that ends with 5 and the same thing repeats on,
The series goes as 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96.
On counting the number of terms present in the sequence, we get 20.
No.of numbers in this sequence which are below 100 by actual counting are 20.
4) Without actual counting.
Yes! We can do that. If we observe the sequence, for every range of ten numbers, 2 numbers of them are getting their presence into the series. So, below hundred, in ten 10 ranges (1-10, 11-20, 21-30,..., 91-100), we get
10(no.of entries) = 10(2) = 20 numbers.
So, the count of numbers in this sequence which are below 100 WITHOUT actual counting is 20.
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