Arithmetic Prog...

$${\log _5}2,\,\,{\log _6}\,2,\,\,{\log _{12}}\,\,2\,\,$$ are in 

$$
\ln \text { an } A . P \mathrm{t}_{7}=4, \mathrm{d}=-4 \text { and } n=101, \text { find the value of } a
 $$

The average of certain first consecutive even number is $$101$$. Find their sum?

In an A.P., $$S_p=q$$ and $$S_q=p$$, where $$ S_r $$ denotes the sum of the first $$r$$ terms of an A.P. Then, the value of $$S_{p+q}$$ is

Which of the following are APs ? If they an AP. find the common difference of and  write three more terms.

If $$a_1, a_2, a_3, ....$$ is an A.P. such that $$a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225$$ then $$a_1+a_2+a_3+ ... +a_{23}+a_{24}$$ is equal to-

The sum of digits of all numbers from 1 to 300 is equal to 

Let $$(1+x)^n=\sum _{ r=0 }^{ n }{ { a }_{ r }{ x }^{ r } } $$. Then $$(1+\frac {a_1}{a_0})(+\frac {a_2}{a_1})....(1+\frac {a_n}{a_{n-1}})$$ is equal to:

Choose the correct alternative for questions:
For an A.P., if d=11, then $${ t }_{ 17 }-{ t }_{ 15 }=?$$

What is the common difference of an A.P. whose nth term is $${ t }_{ n }=2n-4$$