The sum of the first $20$ terms common between the series $3 +7 + 1 1 + 15+ ... ......$ and $1 +6+ 11 + 16+ ......$, is

When $9^{th}$ term of $A.P$ is divided by its $2^{nd}$ term then quotient is $5$ and when $13^{th}$ term is divided by $6^{th}$ term then quotient is $2$ and Remainder is $5$ then find first term of $A.P.$

If $a_1, a_2, a_3 …………$ an are in $A.P$ and $a_1 + a_4 + a_7 + …………… + a_{16} = 114$, then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

If $\log _{3} 2, \log _{3}\left(2^{x}-5\right), \log _{3}\left(2^{x}-\frac{7}{2}\right)$ are in an arithmetic progression, then the value of $x$ is equal to $.....$

The income of a person is $Rs. \,3,00,000,$ in the first year and he receives an increase of $Rs.\,10,000$ to his income per year for the next $19$ years. Find the total amount, he received in $20$ years.