If $n$ arithmetic means are inserted between $a$ and $100$ such that the ratio of the first mean to the last mean is $1:7$ and $a+n=33$,then the value of $n$ is

Insert $6$ numbers between $3$ and $24$ such that the resulting sequence is an $A.P.$

What is the sum of all integers between $81$ and $719$ that are divisible by $5$?

Let $a_1, a_2, a_3, \ldots, a_{100}$ be an arithmetic progression with $a_1=3$ and $S_p=\sum_{i=1}^p a_i, 1 \leq p \leq 100$. For any integer $n$ with $1 \leq n \leq 20$,let $m=5n$. If $\frac{S_m}{S_n}$ does not depend on $n$,then $a_2$ is

Consider an $A$.$P$.: $a_1, a_2, \dots, a_n$,with $a_1 > 0$. If $a_2 - a_1 = -\frac{3}{4}$,$a_n = \frac{1}{4} a_1$,and $\sum_{i=1}^n a_i = \frac{525}{2}$,then $\sum_{i=1}^{17} a_i$ is equal to:

Four numbers are in arithmetic progression. The sum of the first and last term is $8$ and the product of both middle terms is $15$. The least number of the series is