If $a,\;b,\;c,\;d,\;e,\;f$ are in $A.P.$, then the value of $e - c$ will be
$2(c - a)$
$2(f - d)$
$2(d - c)$
$d - c$
Let the sequence $a_{n}$ be defined as follows:
${a_1} = 1,{a_n} = {a_{n - 1}} + 2$ for $n\, \ge \,2$
Find first five terms and write corresponding series.
If the angles of a quadrilateral are in $A.P.$ whose common difference is ${10^o}$, then the angles of the quadrilateral are
If $\frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}$ is the $A.M.$ between $a$ and $b,$ then find the value of $n$.
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 $n$ be odd or even, then the sum of $n$ terms of the series $1 - 2 + $ $3 - $$4 + 5 - 6 + ......$ will be