Find the ${20}^{\text{th }}$ term and the sum of $20$ terms of the series:

$2\times 4+4\times 6+6\times 8+\dots$

If Sum the following series $3+5+9+15+23+\dots$  to $n$ terms is $\frac{kn\left[n^a+b\right]}{c}$, then $k+a+b+c=$

The Sum of $2+5+10+17+26+\dots$  to $n$ terms is $\frac{n\left(a{n}^2+bn+c\right)}{6}$. Hence, find $a+b+c$.

If the sum of $1+3+7+13+21+\dots$ to $n$ terms is $n\left(\frac{n^2+a}{b}\right)$ then find $a+b$.

If Sum the following series $3+7+14+24+37+\dots$ to $n$ terms is $\frac{kn}{a}\left[b{n}^2+cn+d\right]$, then $k+a+b+c+d=$

Sum the following series to $n$ terms:

$1+3+6+10+15+\dots$

If the sum of $1+4+13+40+121+\dots$ to $n$ terms is $\left(\frac{k^{n+1}-k-2n}{4}\right)$ then find the value of $k$.

If the sum of the series $4+6+9+13+18+\dots$ to $n$ terms is $\frac{n}{6}\left(a{n}^2+bn+c\right)$ then find the value of $a+b+c$.

If the sum of the series $2+4+7+11+16+\dots$ to $n$ terms is $\frac{n}{6}\left(a{n}^2+bn+c\right)$ then find the value of $a+b+c$.