1. **State the problem:** We are given the 5th term ($a_5$) and the 11th term ($a_{11}$) of an arithmetic progression (AP) and need to find the 8th term ($a_8$). 2. **Recall the formula for the $n$th term of an AP:** $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term and $d$ is the common difference. 3. **Write equations for the given terms:** $$a_5 = a_1 + 4d = 22$$ $$a_{11} = a_1 + 10d = 48$$ 4. **Find $d$ by subtracting the first equation from the second:** $$a_{11} - a_5 = (a_1 + 10d) - (a_1 + 4d) = 6d = 48 - 22 = 26$$ $$\Rightarrow d = \frac{26}{6} = \frac{13}{3}$$ 5. **Find $a_1$ by substituting $d$ back into one of the equations:** $$a_5 = a_1 + 4d = 22$$ $$a_1 = 22 - 4 \times \frac{13}{3} = 22 - \frac{52}{3} = \frac{66}{3} - \frac{52}{3} = \frac{14}{3}$$ 6. **Find the 8th term $a_8$:** $$a_8 = a_1 + 7d = \frac{14}{3} + 7 \times \frac{13}{3} = \frac{14}{3} + \frac{91}{3} = \frac{105}{3} = 35$$ **Final answer:** The 8th term of the arithmetic progression is **35**.