The first term of an $A.P.$ of consecutive integers is ${p^2} + 1$ The sum of $(2p + 1)$ terms of this series can be expressed as
${(p + 1)^2}$
${(p + 1)^3}$
$(2p + 1){(p + 1)^2}$
${p^3} + {(p + 1)^3}$
Let $a_n$ be a sequence such that $a_1 = 5$ and $a_{n+1} = a_n + (n -2)$ for all $n \in N$, then $a_{51}$ is
If sum of $n$ terms of an $A.P.$ is $3{n^2} + 5n$ and ${T_m} = 164$ then $m = $
If the sum of first $11$ terms of an $A.P.$, $a_{1} a_{2}, a_{3}, \ldots$is $0\left(\mathrm{a}_{1} \neq 0\right),$ then the sum of the $A.P.$, $a_{1}, a_{3}, a_{5}, \ldots, a_{23}$ is $k a_{1},$ where $k$ is equal to
Jairam purchased a house in Rs. $15000$ and paid Rs. $5000$ at once. Rest money he promised to pay in annual installment of Rs. $1000$ with $10\%$ per annum interest. How much money is to be paid by Jairam $\mathrm{Rs.}$ ...................
Let $X$ be the set consisting of the first $2018$ terms of the arithmetic progression $1,6,11$,
. . . .and $Y$ be set consisting of the first $2018$ terms of the arithmetic progression $9, 16, 23$,. . . . . Then, the number of elements in the set $X \cup Y$ is. . . .