Assam Board Solutions for Chapter: Arithmetic Progressions, Exercise 3: Exercise 5.3

In the following $\mathrm{}\mathrm{A}\mathrm{P}$, $a_3=15,\mathrm{}{S}_{10}=125$, find $\mathrm{d}$ and $\mathrm{}{a}_{10}$.
 

In an $\mathrm{}\mathrm{A}\mathrm{P}$, $\mathrm{}d=5,\mathrm{}{S}_9=75$, find $a\mathrm{}$ and $a_9$.
 

In an $\mathrm{}\mathrm{A}\mathrm{P}$,

given $a=2, d=8, S_n=90$, find $n$ and $a_n$.
 

In an $\mathrm{}\mathrm{A}\mathrm{P}$ : $a=8, a_n=62, S_n=210$, find $n$ and $\mathrm{}d$.
 

In an $\mathrm{}\mathrm{A}\mathrm{P}$, given $a_n=4, d=2, S_n=-14$, find $n$ and $\mathrm{}a$.

In an $\mathrm{}\mathrm{A}\mathrm{P}$ :

given $a=3, n=8, S=192$, find $\mathrm{}d$.
 

In an $\mathrm{}\mathrm{A}\mathrm{P}$:

given $\mathrm{}l=28,\mathrm{}S=144$, and there are total $\mathrm{}9$ terms. Find $\mathrm{}a$.

Show that $a_1,\mathrm{}{a}_2,\mathrm{}\dots ,\mathrm{}{a}_n,\dots$ form an $\mathrm{A}\mathrm{P}$ where $a_n$ is defined as $a_n=9-5n$. Also find the sum of the first $\mathrm{}15$ terms.