If $(b+c),(c+a),(a+b)$ are in $H.P$ , then $a^2,b^2,c^2$ are in.......

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $\mathrm{S}_{10}=390$ and the ratio of the tenth and the fifth terms is $15: 7$, then $S_{15}-S_5$ is equal to:

If the sum of first $p$ terms of an $A.P.$ is equal to the sum of the first $q$ terms, then find the sum of the first $(p+q)$ terms.

What is the $20^{\text {th }}$ term of the sequence defined by

$a_{n}=(n-1)(2-n)(3+n) ?$

The value of $\sum\limits_{r = 1}^n {\log \left( {\frac{{{a^r}}}{{{b^{r - 1}}}}} \right)} $ is

Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=\frac{2 n-3}{6}$