Question

Find the next number in the following pattern:
1 5 3 7 5 9 7 ...

Answer 1

Answer: The next number in the given pattern is 11.

Step-by-step explanation: We are given to find the next number in the following pattern :

1 5 3 7 5 9 7 . . .

Let a(n) denotes the n-th number of the give pattern.

Then, we see the following rule if followed by the consecutive terms :

`a(1)=1\\\\a(2)=5=1+4=a(1)+4,\\\\a(3)=3=5-2=a(2)-2,\\\\a(4)=7=3+4=a(3)+4,\\\\a(5)=5=7-2=a(4)-2,\\\\a(6)=9=5+4=a(5)+4,\\\\a(7)=7=9-2=a(6)-2,~~~.~~~.~~~.`

Therefore, the next term will be the sum of the 7-th number and 4. That is

`a(8)=a(7)+4=7+4=11.`

Thus, the next number in the given pattern is 11.