If ${S_n} = nP + \frac{1}{2}n(n - 1)Q$, where ${S_n}$ denotes the sum of the first $n$ terms of an $A.P.$, then the common difference is
$P + Q$
$2P + 3Q$
$2Q$
$Q$
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.
If sum of $n$ terms of an $A.P.$ is $3{n^2} + 5n$ and ${T_m} = 164$ then $m = $
Find the $17^{\text {th }}$ and $24^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=4 n-3$
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 $A.P.$
Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$