Arithmetic Prog...

$$30$$ trees are planted in a straight line at intervals of $$5\ m.$$ To water them, the gardener needs to bring water for each tree, separately from a well, which is $$10\ m$$ from the first tree in line with the trees. How far will he have to walk in order to water all the trees beginning with the first tree? Assume that he starts from the first well, and he can carry enough water to water only one tree at a time. 

Identify the progression:

Let $$S_n$$ denote the sum of the first $$'n'$$ terms of an A.P. $$S_{2n} = 3S_n$$. Then, the ratio $$\dfrac{S_{3n}}{S_n}$$ is equal to :

If $$\displaystyle \frac{3+5+7+......+ n(terms)}{5+8+11+.....+ 10(terms)}=7$$, then the value of $$n$$ is 

The sum up to $$9$$ terms of the series $$\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{6}+ ...$$ is

If $$S=\cfrac { n }{ 2 } [2a+(n-1)d]$$ ; find $$d$$ , when $$a=8, S=380$$ and $$n=10$$.

A sprinter runs 6 meters in the first second of a certain race and increase her speed by 25 cm/sec. in each succeeding second. (This means that she goes 6m 25 cm. the second second, 6m 50 cm. the third second, and so on.) How far does she go during the eight second?

The $$p^{th}$$ and $$q^{th}$$ terms an $$A.P$$ are respectively $$a$$ and $$b.$$ Then sum of $$(p+q)$$ terms is

STATEMENT - $$1$$ : The sum of first $$11$$ terms of the A.P: $$2, 6, 10, 14,\dots$$ is $$242.$$
STATEMENT - $$2$$ : The sum of first $$n$$ terms of the A.P. is given by $$S_n = \dfrac{n}{2} [2a + (n-1)d]$$

The sum of 24 terms of the series $$1, -3, 4, -6, 7, -9, 10, ...$$ is