Arithmetic Prog...

The common difference of A.P.: $$1, -1, -3, ....$$ is _______

If $$a, b$$ and $$c$$ arc in arithmetic progression then $$\dfrac{b- a}{c - b}$$ is equal to

Firs term of an arithmetic progression is $$2$$. If the sum of its first five terms is equal to one-fourth of the sum of the next five terms, then the sum of its first $$30$$ terms is

$$(n-2)^{th}$$ term of an arithmetic progression will be __________.

If $$S_{r}$$ denotes the sum of $$r$$ terms of an AP and $$\dfrac {S_{a}}{a^{2}} = \dfrac {S_{b}}{b^{2}} = c$$ then $$S_{c}$$ is

Find the sum of the first $$25$$ terms of an A.P whose $$n$$th term is given by $${a}_{n}=8-3n$$

If $$\dfrac{2}{3},k, \dfrac{5}{8}$$ are in AP, find the value of k.

Find the number of terms of the A.P $$-12,-9,-6,.....,21$$. If $$1$$ is added to each term of this A.P., then find the sum of all terms of the A.P thus obtained.

There are $$20$$ rows of seats in a conference hall with $$20$$ seats in the first row, $$21$$ seats in the second row, $$22$$ seats in the third row and so on. In total, how many seats are there in the conference hall?

Find the sum of the first $$15$$ terms of the sequence having $$n$$th term as
$${ y }_{ n }=9-5n\quad $$