Neha Tyagi and Amit Rastogi Solutions for Chapter: Arithmetic Progressions, Exercise 4: Exercise

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

Find the sum of the integers between $100$ and $200$ that are divisible by $9$.

Find the sum of the integers between $100$ and $200$ that are not divisible by $9.$.

The ratio of the ${11}^{\mathrm{th}}$ term to the ${18}^{\mathrm{th}}$ term of an AP is $2:3.$ Find the ratio of the $5^{\mathrm{th}}$ term to the ${21}^{\mathrm{st}}$ term and also the ratio of the sum of the first five terms to the sum of the first $21$ terms.

Show that the sum of an AP whose first term is $a$, the second term $b$ and the last term $c$, is equal to $\frac{(a+c)(b+c-2a)}{2(b-a)}.$

Solve the equation $-4+(-1)+2+...+x=437.$

Jaspal Singh repays his total loan of $\mathrm{Rs}. 118000$ by paying every month starting with the first instalment of $\mathrm{Rs}. 1000$. If he increases the instalment by $\mathrm{Rs}. 100$ every month, what amount will be paid by him in the $30\mathrm{th}$ instalment? What amount of loan does he still have to pay after the $30\mathrm{th}$ instalment?

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 $2 \mathrm{m}$. 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 time. How much distance she did cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?