Find the sum of those integers from $1$ to $500$ which are multiples of $2$ or $5$.

In an $AP$,given $a=2, d=8, S_{n}=90$,find $n$ and $a_{n}$.

Find four numbers in $A.P.$ such that their sum is $36$ and the product of means ($2^{nd}$ and $3^{rd}$ term) exceeds the product of extremes ($1^{st}$ and $4^{th}$ term) by $32.$

An $AP$ consists of $37$ terms. The sum of the three middle most terms is $225$ and the sum of the last three is $429$. Find the $AP$.

Five years ago,the sum of the ages of four persons was $60$ years. The sum of the present ages of those four persons is $\ldots \ldots \ldots \ldots$ years.

The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have $27$ flags to be fixed at intervals of every $2 \,m$. The flags are stored at the position of the middle-most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much total distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag? (in $m$)