Question

Write the next 3 numbers in this pattern. Then describe the rule for this pattern in an nth expression.

11 , 101 , 1001 , 10001,…

Answer 1

An=10^n + 1 is the expression for the nth term.

Next three terms:

100001

1000001

10000001

Explanation:

The number ot 0's imcrease between the two 1's starting at no zeros, 1 zero, two zeros, and so on...

So the next terms are 100001, 1000001, 10000001 and that's without finding the formula.

Now let's find the formula:

A1=11=10+1

A2=101=100+1

A3=1001=1000+1

Notice we have increasing powers of 10 and then just adding 1.

A1=10^1 +1

A2=10^2 +1

A3=10^3 +1

....

An=10^n +1