Sequences and Series question bank (Maths)

Let the arithmetic mean of $\frac{1}{\mathrm{a}}$ and $\frac{1}{\mathrm{~b}}$ be $\frac{5}{16}, \mathrm{a}\gt 2$. If $\alpha$ is such that $\mathrm{a}, 4, \alpha, \mathrm{~b}$ are in A.P., then the equation $\alpha x^{2}-a x+2(\alpha-2 b)=0$ has:

Let $a_{1}, a_{2}, a_{3}, a_{4}$ be an A.P. of four terms such that each term of the A.P. and its common difference $l$ are integers. If $a_{1}+a_{2}+a_{3}+a_{4}=48$ and $a_{1} a_{2} a_{3} a_{4}+l^{4}=361$, then the largest term of the A.P. is equal to