The sums of $n$ terms of three $A.P.'s$ whose first term is $1$ and common differences are $1, 2, 3$ are ${S_1},\;{S_2},\;{S_3}$ respectively. The true relation is
${S_1} + {S_3} = {S_2}$
${S_1} + {S_3} = 2{S_2}$
${S_1} + {S_2} = 2{S_3}$
${S_1} + {S_2} = {S_3}$
If the ${p^{th}}$ term of an $A.P.$ be $\frac{1}{q}$ and ${q^{th}}$ term be $\frac{1}{p}$, then the sum of its $p{q^{th}}$ terms will be
If $2x,\;x + 8,\;3x + 1$ are in $A.P.$, then the value of $x$ will be
If sum of $n$ terms of an $A.P.$ is $3{n^2} + 5n$ and ${T_m} = 164$ then $m = $
If $\frac{1}{{b - c}},\;\frac{1}{{c - a}},\;\frac{1}{{a - b}}$ be consecutive terms of an $A.P.$, then ${(b - c)^2},\;{(c - a)^2},\;{(a - b)^2}$ will be in
Maximum value of sum of arithmetic progression $50, 48, 46, 44 ........$ is :-