If $a,\;b,\;c$ are in $A.P.$, then $\frac{1}{{bc}},\;\frac{1}{{ca}},\;\frac{1}{{ab}}$ will be in

Find the $17^{\text {th }}$ and $24^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=4 n-3$

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 $TRUE$ ?

$(A)$ $T_{20}=1604$

$(B)$ $\sum_{ k =1}^{20} T_{ k }=10510$

$(C)$ $T_{30}=3454$

$(D)$ $\sum_{ k =1}^{30} T_{ k }=35610$

The ratio of the sums of first $n$ even numbers and $n$ odd numbers will be

Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=\frac{n}{n+1}$

Find the $20^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=\frac{n(n-2)}{n+3}$