Final answer:
To find the 10th term in the sequence, identify the common ratio by dividing the second term by the first, then apply this ratio repeatedly. The 10th term is approximately 3.308946 after multiplying the first term by the common ratio to the power of 9.
Step-by-step explanation:
To find the 10th term of the sequence 82, 57.4, 40.18..., we first need to identify the pattern or rule that the sequence follows. By examining the differences between the terms, we can infer that the sequence is decreasing at a changing rate. To find this rate, we look at the differences between consecutive terms:
- 57.4 - 82 = -24.6
- 40.18 - 57.4 = -17.22
It seems that each term is being multiplied by a common ratio to get the next term. The ratio can be found by dividing the second term by the first term:
Ratio = 57.4 / 82 ≈ 0.7
Once the ratio is identified, we can apply it repeatedly to find subsequent terms. To find the 10th term, we would continue the pattern, multiplying each term by 0.7 to get the next:
10th term = 82 * (0.7)^9
After calculating this, the 10th term in the sequence is approximately:
10th term ≈ 82 * 0.040353
10th term ≈ 3.308946