Question

Write a short description of the pattern in this sequence of six numbers and then follow that pattern to write the next three numbers in the sequence 1/5 2/8 3/11 4/14 5/17 6/20

Answer 1

Answer: The next three terms are
`(7)/(23),(8)/(26),(9)/(29)`

Explanation:

Since we have given that

`(1)/(5),(2)/(8),(3)/(11),(4)/(14),(5)/(17),(6)/(20)`

After analyzing the above pattern, we get that

In numerator , numbers are run in consecutive manner.

In denominator, number is added to 3 to get the next term.

So, the general form would be
`(n)/(3n+2)`

So, the next three terms would be

`(7)/(3* 7+2)=(7)/(23)\\\\(8)/(3* 8+2)=(8)/(26)\\\\(9)/(3* 9+2)=(9)/(29)`

Hence, the next three terms are

`(7)/(23),(8)/(26),(9)/(29)`