SOLUTION: Start with the number 1 and create the sequence: 1,2,4,8,16,22,24,28 where each number is the sum of the previous number and its final digit. How many numbers in the sequence are

Question 1182732: Start with the number 1 and create the sequence:
1,2,4,8,16,22,24,28
where each number is the sum of the previous number and its final digit. How many numbers in the sequence are less than 1000?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Write out the next 10-20 numbers in the sequence....
1, 2, 4, 8, 16, 22, 24, 28, 36, 42, 44, 48, 56, 62, 64, 68, 76, 82, 84, 88, 96, ...

... and look for a pattern:
1, 2, 4, 8, 16 // 22, 24, 28, 36 // 42, 44, 48, 56 // 62, 64, 68, 76 // 82, 84, 88, 96 // ...

5 numbers less than 19
4 more numbers 20 to 39
4 more number 40 to 59
4 more numbers 60 to 79
4 more numbers 80 to 99
...

It should be clear that the pattern will continue.

There are 4 numbers in the sequence in every interval of 20 consecutive integers, except there is 1 additional number in the sequence among the first 20 integers.

The number of intervals of length 20 up to 1000 is 1000/20 = 50; so

ANSWER: the number of numbers in the sequence less than 1000 is 50(4)+1 = 201.

RELATED QUESTIONS
a sequence of numbers starts with 1, 2 and 3. The fourth number of the sequence is the... (answered by ewatrrr)

1,2,4,8,16,22,24,28... where each number is the sum of the previous number and its... (answered by Edwin McCravy)

1. Describe a pattern in each sequence. What are the next two terms of each sequence? (answered by KMST)

A six-sided die with sides numbered 1 through 6 is tossed 4 times . What is the largest... (answered by ikleyn)

To calculate permutations of the golden ratio start by writing the first 20 numbers of... (answered by solver91311)

A number sequence is as follows: 4, 8, 12, 16, 20, 24, .... If 4 is the 1st number in the (answered by fractalier)

A sequence starting with 1 and is formed by doubling the previous number and then... (answered by richwmiller)

The sum of a negative number, 1/4 of the negative number, and 7/16 of the negative number (answered by Fombitz)

The sum of a negative number, 1/4 of the negative number, and 7/16 of the negative number (answered by ankor@dixie-net.com)