Question

Write a recursive formula for finding the nth term of each arithmetic sequence. 15.75, 14.25, 12.75, ...

answers:
1) A1 = 15.75, An = An-1 +1.5
2)A1 = 12.75, An = An-1 -1.5
3)A1 = 11.25, An = An-1 +1.5
4)A1 = 15.75, An = An-1 -1.5

Answer 1

The recursive formula for the arithmetic sequence 15.75, 14.25, 12.75, ... is A1 = 15.75, An = An-1 - 1.5 where the first term is 15.75 and each subsequent term is 1.5 less than the previous term.

Step-by-step explanation:

To write a recursive formula for finding the nth term of the given arithmetic sequence, we must first determine the common difference by subtracting any term from the one that comes after it. In this case, the difference between consecutive terms is -1.5 (for example, 14.25 - 15.75).

Therefore, the recursive formula for the arithmetic sequence 15.75, 14.25, 12.75, ... is:

• A1 = 15.75, which is the first term.
• An = An-1 - 1.5, which expresses that the nth term is found by subtracting 1.5 from the previous term.

With this formula, each term after the first is generated by taking the previous term and subtracting 1.5.