Manipur Board Solutions for Chapter: Arithmetic Progression (AP), Exercise 2: EXERCISE 6.2

Find the sum of the first $22$ terms of an AP whose $8^{th}$ and ${16}^{th}$ terms are respectively $37$ and $85$.

The sum of the first 7 terms of an AP is 10 and that of the next 7 terms is 17. Find the first term and the common difference of the AP.

Find the sum of the first $50$ terms of an AP whose ${\mathrm{n}}^{\mathrm{th}}$ term is $3-2\mathrm{n}$.

Find the first term and the common difference of an AP if the sum of the first $\mathrm{n}$ term is $\frac{\mathrm{n}\left(5\mathrm{n}+7\right)}{12}$.

In an AP, if the sum of the first $\mathrm{m}$ terms is equal to $\mathrm{n}$ and that of the first $\mathrm{n}$ terms is equal to $\mathrm{m}$, then prove that the sum of the first $\left(\mathrm{m}+\mathrm{n}\right)$ terms is $-(\mathrm{m}+\mathrm{n})$.

The sum of the first $\mathrm{n}, 2\mathrm{n}, 3\mathrm{n}$ terms of an AP are ${\mathrm{S}}_1, {\mathrm{S}}_2, {\mathrm{S}}_3$ respectively. Show that ${\mathrm{S}}_3=3({\mathrm{S}}_2-{\mathrm{S}}_1)$.

A man repays a debt of $₹4860$ by paying $₹30$ in the first month and then increases the amount by $₹15$ every month. How long will it take him to clear the debt (Assume that no interest is charged)?

A manufacturer of radio sets produced $600$ units in the third year and $700$ units in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find the production in the first year and also the total production in $8$ years.