Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$, then its $4^{th}$ term is

  • [JEE MAIN 2014]
  • A

    $8$

  • B

    $16$

  • C

    $20$

  • D

    $24$

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If the sum of first $n$ terms of an $A.P.$ is $c n^2$, then the sum of squares of these $n$ terms is

  • [IIT 2009]

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Let the sequence $a_{n}$ be defined as follows:

${a_1} = 1,{a_n} = {a_{n - 1}} + 2$ for $n\, \ge \,2$

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