Welcome back — been a while! Let's pick up where you left off. Step 1: Set up equations for the given terms. The formula for the $n$-th term of an arithmetic progression is $a_n = a_1 + (n-1)d$, where $a_1$ is the first term and $d$ is the common difference. For the third term ($a_3 = 9$): $$a_3 = a_1 + (3-1)d$$ $$9 = a_1 + 2d \quad (*)$$ For the ninth term ($a_9 = 27$): $$a_9 = a_1 + (9-1)d$$ $$27 = a_1 + 8d \quad (**)$$ Step 2: Solve the system of equations to find $a_1$ and $d$. Subtract equation $()$ from equation $(*)$: $$(a_1 + 8d) - (a_1 + 2d) = 27 - 9$$ $$6d = 18$$ $$d = \frac{18}{6}$$ $$d = 3$$ Substitute $d=3$ into equation $(*)$: $$9 = a_1 + 2(3)$$ $$9 = a_1 + 6$$ $$a_1 = 9 - 6$$ $$a_1 = 3$$ Step 3: Find the fifth term ($a_5$). Using the formula $a_n = a_1 + (n-1)d$ with $n=5$, $a_1=3$, and $d=3$: $$a_5 = a_1 + (5-1)d$$ $$a_5 = 3 + 4(3)$$ $$a_5 = 3 + 12$$ $$a_5 = 15$$ The fifth term is $\boxed{\text{15}}$. Send me the next one 📸