Sequences and S...

Geometric mean of $$7,\ { 7 }^{ 2 },\ { 7 }^{ 3 }....{ 7 }^{ n }$$ is

Suppose $$a_2,a_3,a_4,a_5,a_6,a_7$$ are integers such that
$$\dfrac {5}{7}=\dfrac {a_2}{2!}+\dfrac {a_3}{3!}+\dfrac {a_4}{4}+\dfrac {a_5}{5!}+\dfrac {a_6}{6!}+\dfrac{a_7}{7!}$$
where $$0 \le a < j$$ for $$ j=2,4,5,6,7.$$ The sum $$a_2+a_3+a_4+a_5+a_6+a_7$$ is 

The value of the sum $$1.2.3+2.3.4+3.4.5+.......$$ upto n terms=

If $$x\in R$$, find the minimum value of the expression $$3^x+3^{1-x}$$.

The sum of the first n terms of the series $$1^2 + 2.2^2 + 3^2 + 2.4^2 + 5^2 + 2.6^2 +$$ ...... is  $$\dfrac{n(n + 1)^2}{2}$$  when n is even.When n is odd the sum is -

If $$28\div 11 = 8, 39\div 21 = 7, 45\div 27 = 4$$, then $$95\div 25 = ?$$

The odd natural numbers have been divided in groups as $$(1, 3); (5, 7, 9, 11); (13, 15, 17, 19, 21, 23); .....$$ Then the sum of numbers in the $$10^{th}$$ group is

In a row of girls, Mridula is $$18^{th}$$ from the right and Sanjana is $$18^{th}$$ from the left. If both of them interchange their position, Sanjana becomes $$25^{th}$$ from the left, how many girls are there in the row?

A series whose $$n^{th}$$ term is $$\lgroup \dfrac{n}{x}\rgroup + y$$, the sum of r terms will be 

Choose the correct answer from the alternatives given.
A loss of $$20%$$ is incurred when $$6$$ articles are sold for a rupee. To gain $$20% $$ how many articles should be sold for a rupee?