Question

Given the sequence 11, 111, 211, 311, 411 Determine its nᵗʰ term

Answer 1

The nth term of the sequence 11, 111, 211, 311, 411 is obtained by the formula 'T(n) = 11 + 100(n - 1)' which simplifies to 'T(n) = 100n - 89'. This is because each term in the sequence increases by 100 from the previous term.

Step-by-step explanation:

The given sequence is 11, 111, 211, 311, 411 which suggests that each term after the first increases by 100 from the previous term. To find the nth term of this sequence, we can observe that the sequence starts with 11 and adds 100(n-1) to it, where n is the position of the term in the sequence.

The formula for the nth term can be derived as follows:

1. Start with the first term which is 11.
2. If we add 100 to it, we get the second term which is 111. Notice the pattern of adding 100 more than the previous term.
3. To find the nth term, we would have added 100 to the first term (n-1) times. Thus, the formula for the nth term is: First term + 100(n-1)
4. The nth term formula for this sequence is 11 + 100(n - 1).

If we simplify this, we get T(n) = 11 + 100n - 100, which can further be simplified to T(n) = 100n - 89. This is the formula for the nth term of the sequence.