Four numbers are in an arithmetic progression. The sum of the first and last terms is $8$ and the product of the two middle terms is $15$. What is the smallest number in the sequence?

If the first,second and last terms of an $A.P.$ are $a, b$ and $2a$ respectively,then its sum is:

The sequence $\frac{5}{\sqrt{7}}, \frac{6}{\sqrt{7}}, \sqrt{7}, \dots$ is

The number of terms in the series $101 + 99 + 97 + \dots + 47$ is

For $p, q \in R$,consider the real-valued function $f(x) = (x - p)^2 - q$,where $x \in R$ and $q > 0$. Let $a_1, a_2, a_3, a_4$ be in an arithmetic progression with mean $p$ and a positive common difference $d$. If $|f(a_i)| = 500$ for all $i = 1, 2, 3, 4$,then the absolute difference between the roots of $f(x) = 0$ is:

If $\frac{1}{p+q}, \frac{1}{r+p}$,and $\frac{1}{q+r}$ are in Arithmetic Progression $(AP)$,then which of the following is true?