If the $9^{th}$ term of an $A.P.$ be zero, then the ratio of its $29^{th}$ and $19^{th}$ term is
$1:2$
$2:1$
$1:3$
$3:1$
Let $a_1, a_2, a_3, \ldots$ be an arithmetic progression with $a_1=7$ and common difference $8$ . Let $T_1, T_2, T_3, \ldots$ be such that $T_1=3$ and $T_{n+1}-T_n=a_n$ for $n \geq 1$. Then, which of the following is/are $TRUE$ ?
$(A)$ $T_{20}=1604$
$(B)$ $\sum_{ k =1}^{20} T_{ k }=10510$
$(C)$ $T_{30}=3454$
$(D)$ $\sum_{ k =1}^{30} T_{ k }=35610$
If the first term of an $A.P.$ is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms, then the common difference of this $A.P.$ is :
If all interior angle of quadrilateral are in $AP$ . If common difference is $10^o$ , then find smallest angle ?.....$^o$
Insert $6$ numbers between $3$ and $24$ such that the resulting sequence is an $A.P.$
Let $\frac{1}{{{x_1}}},\frac{1}{{{x_2}}},\frac{1}{{{x_3}}},.....,$ $({x_i} \ne \,0\,for\,\,i\, = 1,2,....,n)$ be in $A.P.$ such that $x_1 = 4$ and $x_{21} = 20.$ If $n$ is the least positive integer for which $x_n > 50,$ then $\sum\limits_{i = 1}^n {\left( {\frac{1}{{{x_i}}}} \right)} $ is equal to.