Find the $7^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=\frac{n^{2}}{2^{n}}$

Vedclass pdf generator app on play store
Vedclass iOS app on app store

Substituting $n=7,$ we obtain

$a_{7}=\frac{7^{2}}{2^{7}}=\frac{49}{128}$

Similar Questions

If the ${p^{th}}$ term of an $A.P.$ be $q$ and ${q^{th}}$ term be $p$, then its ${r^{th}}$ term will be

If the sum of first $n$ terms of an $A.P.$ is $c n^2$, then the sum of squares of these $n$ terms is

  • [IIT 2009]

If the sum of the first $n$ terms of a series be $5{n^2} + 2n$, then its second term is

If $a_1 , a_2, a_3, . . . . , a_n, ....$ are in $A.P.$ such that $a_4 - a_7 + a_{10}\, = m$, then the sum of first $13$ terms of this $A.P.$, is .............. $\mathrm{m}$

  • [JEE MAIN 2013]

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 $TRUE$ ?

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

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

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

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

  • [IIT 2022]