Question

Given the sequence -5, -25, -45, -65, determine the arithmetic sequence using the recursive formula b(n)=b(n−1)+d, where d is the common difference.

Answer 1

The given sequence -5, -25, -45, -65 represents an arithmetic sequence with a common difference of -20. To determine the arithmetic sequence using the recursive formula b(n) = b(n-1) + d, where d is the common difference, substitute the value of n into the formula.

Step-by-step explanation:

The given sequence -5, -25, -45, -65 represents an arithmetic sequence with a common difference of -20. To determine the arithmetic sequence using the recursive formula b(n) = b(n-1) + d, where d is the common difference:

1. The first term of the sequence b(1) is given as -5.
2. To find the second term b(2), substitute n = 2 into the formula: b(2) = -5 + (-20) = -25.
3. To find the third term b(3), substitute n = 3 into the formula: b(3) = -25 + (-20) = -45.
4. Continue this process to find subsequent terms of the sequence.