1. **State the problem:** We need to find the 20th term of an arithmetic sequence where the 3rd term is 19.6 and the 7th term is 48.8. 2. **Recall the formula for the nth term of an arithmetic sequence:** $$a_n = a_1 + (n-1)d$$ where $a_n$ is the nth term, $a_1$ is the first term, and $d$ is the common difference. 3. **Use the given terms to set up equations:** - For the 3rd term: $$a_3 = a_1 + 2d = 19.6$$ - For the 7th term: $$a_7 = a_1 + 6d = 48.8$$ 4. **Subtract the first equation from the second to find $d$:** $$a_7 - a_3 = (a_1 + 6d) - (a_1 + 2d) = 48.8 - 19.6$$ $$6d - 2d = 29.2$$ $$4d = 29.2$$ $$d = \frac{29.2}{4}$$ $$d = 7.3$$ 5. **Find $a_1$ using $a_3 = a_1 + 2d = 19.6$:** $$a_1 = 19.6 - 2 \times 7.3$$ $$a_1 = 19.6 - 14.6$$ $$a_1 = 5$$ 6. **Find the 20th term using $a_{20} = a_1 + 19d$:** $$a_{20} = 5 + 19 \times 7.3$$ $$a_{20} = 5 + 138.7$$ $$a_{20} = 143.7$$ **Final answer:** The 20th term of the sequence is $143.7$.