Question

1,6, 11, 16... is the requence in which 1 or 6 comes in the right end of the Number
a) Write next five terms of this sequence
6) which is the largest two digit term of this sequence,
C) How many numbers are there below in 100 in this sequence? Find it by actual counting ?
D) can you find it without counting.​

Answer 1

Given data :

Sequence = 1,6, 11, 16,... In which 1 or 6 comes in the right end of the Number.

To find :

1. Next five terms in the sequence.
2. Largest 2 digit term in the sequence.
3. No.of numbers in this sequence which are below 100 by actual counting.
4. 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.

Learn more :

1) odd element in set {8,1,64,75,27}

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2) Odd one out. 65,75,85,95

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3) 10,25,45,54,60,75,80 odd one out .

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