Question

List the first five terms of the sequence. a1 = 10, an = an-1 + an

Answer 1

There appears to be a typo in the recurrence relation provided in the question. Assuming the correct relation is an = an-1 + n, the first five terms of the sequence are 10, 12, 15, 19, and 24.

Step-by-step explanation:

The question seems to have a typo. If we assume that the correct recurrence relation is an = an-1 + n, the first term a1 is given as 10. To find the subsequent terms, we add the position of the term to the previous term. Here are the first five terms:

Sequence:

1. a1 = 10 (Given)
2. a2 = a1 + 2 = 10 + 2 = 12
3. a3 = a2 + 3 = 12 + 3 = 15
4. a4 = a3 + 4 = 15 + 4 = 19
5. a5 = a4 + 5 = 19 + 5 = 24

However, the original recurrence from the question, an = an-1 + an, doesn't lead to a proper sequence as it suggests that a term equals itself plus its previous term, which is not logically possible.

Answer 2

The first five terms of the sequence are 10, 20, 40, 80, 160.respectively, showcasing the exponential growth pattern inherent in the sequence.

Explanation:

The given sequence starts with a₁ = 10. Each subsequent term is calculated by adding the previous term (aₙ₋₁) to the current term (aₙ). Therefore, the second term (a₂) is found by adding 10 (a₁) to itself, resulting in 20. Continuing this pattern, the third term (a₃) is 20 + 20 = 40, the fourth term (a₄) is 40 + 40 = 80, and the fifth term (a₅) is 80 + 80 = 160.

This sequence follows a pattern of doubling the previous term to obtain the next term. Hence, each term is twice the value of the preceding term. Starting with 10, each subsequent term doubles the value, creating an exponential growth pattern in the sequence.

Understanding the formula provided (an = an-1 + an) reveals that each term is the sum of the current term and the preceding term, resulting in a sequence that rapidly increases in value as each term is added.

This results in the first five terms being 10, 20, 40, 80, and 160 respectively, showcasing the exponential growth pattern inherent in the sequence.