Exercise – 3

Find the value of $k$ if sum of the following Arithmetic Progression: $\frac{n^2+1}{n}, n, \frac{n^2-1}{n}, ......$ up to $20$ terms is $\frac{10(2n^2-k)}{n}$

Find the sum of the following Arithmetic Progression:

$\left(1-\frac{1}{n}\right), \left(1-\frac{2}{n}\right), \left(1-\frac{3}{n}\right), ......$ up to $n$ terms.

How many terms will it take to get the sum of $1046.5$ in AP $7, 10\frac{1}{2}, 14, ......$

How many terms of the arithmetic progression $24, 21, 18, ......$ must be taken so that their sum is $78$?

First term of an arithmetic progression is $1$, last term is $11$ and sum is $36$. Find the number of terms and common difference.

First term is $17$ and last term is $350$ in an AP. If common difference is $9$, then how many terms are in it? Find the sum of this progression.

Find the sum of all multiples of $3$ natural numbers between $1$ and $100$.

Find the sum of all odd numbers lying between $0$ and $50$.