Arithmetic Prog...

Find the sum of odd numbers between $$0$$ and $$50$$.

Find the A.P. whose sum to $$n$$ terms is $$2n$$$$^2$$ $$+ n$$

Find the $$S_{15} $$ for an AP whose $$nth$$ term is given by $$a_n$$ $$= 3 + 4n$$.

In an AP, given $$a_n = 4, d = 2, S_n = -14,$$ find $$n$$ and $$a$$.

How many terms of the A.P.: $$9, 17, 25,...$$ must be taken to give a sum of $$636$$?

In an AP,
Given $$l = 28, S = 144$$  and there are total $$9$$ terms. Find $$a$$.

Find the sum of first $$51$$ terms of an AP, whose second and third terms are $$14$$ and $$18$$ respectively.

The $$6^{th}$$ term of an arithmetic progression is $$-10$$ and the $$10^{th}$$ term is $$-26.$$ Determine the $$15^{th}$$ term of the AP.

Write first four terms of the AP, when the first term $$a$$ and the common difference $$d$$ are given as follows $$a = -1.25, d = -0.25.$$

Which term of the AP : $$3,8, 13, 18,.. $$is $$78?$$