1. **State the problem:** We are given an arithmetic progression (AP) where the first term $a_1 = 8$ and the 21st term $a_{21} = 108$. We need to find the 7th term $a_7$. 2. **Recall the formula for the $n$th term of an AP:** $$a_n = a_1 + (n-1)d$$ where $d$ is the common difference. 3. **Find the common difference $d$ using the 21st term:** $$a_{21} = a_1 + 20d$$ Substitute the known values: $$108 = 8 + 20d$$ 4. **Solve for $d$:** $$108 - 8 = 20d$$ $$100 = 20d$$ $$d = \frac{100}{20} = 5$$ 5. **Find the 7th term $a_7$ using the formula:** $$a_7 = a_1 + 6d = 8 + 6 \times 5 = 8 + 30 = 38$$ **Final answer:** The 7th term of the AP is $38$.