To find the eleventh term of the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ..., we need to determine the pattern or rule that governs the sequence.

Pattern of the Sequence:
Observing the given sequence, we can see that each term is obtained by adding the previous two terms. This pattern is known as the Fibonacci sequence.

- The first term is 1.
- The second term is also 1.
- The third term is the sum of the first two terms, which is 2.
- The fourth term is the sum of the second and third terms, which is 3.
- The fifth term is the sum of the third and fourth terms, which is 5.
- And so on...

We can express this pattern mathematically using the following formula:

Fn = Fn-1 + Fn-2

where Fn represents the nth term of the sequence.

Finding the Eleventh Term:
To find the eleventh term, we can use the formula mentioned above.

- The tenth term (Fn-1) is 34.
- The ninth term (Fn-2) is 21.

Using the formula, we can calculate the eleventh term:

Fn = Fn-1 + Fn-2
F11 = F10 + F9
F11 = 34 + 21
F11 = 55

Therefore, the eleventh term of the sequence is 55.

Verifying the Answer:
We can verify our answer by listing out the terms of the sequence up to the eleventh term:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55

As we can see, the eleventh term is indeed 55, which matches our calculated answer.

Therefore, the correct answer is option A) 89.

It is a fibonacci sequence in which previous terms is added to get next term.