If ${n^{th}}$ terms of two $A.P.$'s are $3n + 8$ and $7n + 15$, then the ratio of their ${12^{th}}$ terms will be

Let $S_{n}$ denote the sum of first $n$-terms of an arithmetic progression. If $S_{10}=530, S_{5}=140$, then $\mathrm{S}_{20}-\mathrm{S}_{6}$ is equal to :

Find the sum of integers from $1$ to $100$ that are divisible by $2$ or $5.$

Find the sum to $n$ terms of the $A.P.,$ whose $k^{\text {th }}$ term is $5 k+1$

In an $A.P.,$ the first term is $2$ and the sum of the first five terms is one-fourth of the next five terms. Show that $20^{th}$ term is $-112$

If the sum of $n$ terms of an $A.P$. is $2{n^2} + 5n$, then the ${n^{th}}$ term will be