Arithmetic Prog...

The $$6^{th}$$ and $$17^{th}$$ terms of an AP are $$19$$ and $$41$$ respectively, find the $$40^{th}$$ term.

Find the second term and $$nth$$ term of an AP whose $$6th$$ term is $$12$$ and $$8th$$ term is $$22.$$

Find the sum of all multiples of $$9$$ lying between $$300$$ and $$700$$.

Which of the following are $$AP's$$? If they form an $$AP$$, find the common difference $$d$$ and the first $$3$$ terms.
$$3, 3 + $$$$\sqrt{2}$$, $$3 +$$ 2$$\sqrt{2}$$, $$3 + $$3$$\sqrt{2}$$,...

In a garden bed, there are $$23$$ rose plants in the first row, twenty one in the second row, nineteen in the third row and so on. There are five plants in the last row. How many rows are there of rose plants?

The sum of the first $$9$$ terms of an $$A.P$$ is $$81$$ and the sum of it's first $$20$$ terms is $$400.$$ Find the first term, the common difference and the sum upto $$15th$$ term.

A man saved Rs. $$16500$$ in ten years. In each year after the first he saved Rs. $$100$$ more than he did in the preceding year. How much did he save in the first year?

How many terms are there in the AP whose first and fifth terms are $$-14$$ and $$2$$ respectively and the sum of the terms is $$40?$$

Find $$a_{30} -a_{20}$$ for the $$AP$$ $$: a, a + d, a + 2d, a + 3d,...$$

In an AP,
Given $$a =5, d = 3,$$ $$a_n$$ $$= 50$$, find $$n$$ and $$S_n$$.