What type of sequence is x_n={1, 1, 2, 3, 5, 8, 13, 21, ...}?*1 pointHarmonic sequenceArithmetric progressionFibonacci sequenceGeometric progression

The sequence x_n={1, 1, 2, 3, 5, 8, 13, 21, ...} is a Fibonacci sequence.

Here's why:

In a Fibonacci sequence, each number (after the first two) is the sum of the two preceding ones.

If we look at the sequence given:

• The first two numbers are 1 and 1.
• The third number is 1 + 1 = 2.
• The fourth number is 1 + 2 = 3.
• The fifth number is 2 + 3 = 5.
• The sixth number is 3 + 5 = 8.
• The seventh number is 5 + 8 = 13.
• The eighth number is 8 + 13 = 21.

And so on.

This pattern matches the definition of a Fibonacci sequence. Therefore, the sequence x_n={1, 1, 2, 3, 5, 8, 13, 21, ...} is a Fibonacci sequence.