If Sn=2n+5.Find the third term of an AP.​

Question

If Sn=2n+5.Find the third term of an AP.​

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Genesis 1 month 2021-08-12T11:37:42+00:00 2 Answers 0 views 0

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    0
    2021-08-12T11:39:00+00:00

    Given ,

    The sum of first n terms of an AP

    • Sn = 2n + 5

    We know that ,

      \large \boxed{ \rm{a_{(n)} = S_{(n)} - S_{(n - 1)} }}

    Thus ,

     \sf \mapsto a_{(3)} = S_{(3)} - S_{(3 - 1)} \\  \\ \sf \mapsto  a_{3} =2(3) + 5 -  \{ 2(2) + 5\} \\  \\ \sf \mapsto  a_{3} =6 + 5 - 4 - 5 \\  \\ \sf \mapsto  a_{3} =2

     \sf \therefore \underline{The \:  third \:  term \:  of  \: AP \:  is  \: 2}

    0
    2021-08-12T11:39:10+00:00

    Answer

    \rm S_n=2n+5\\\\\implies \rm S_1=2(1)+5\\\\\implies \rm a_1=7\\\\\rm S_2=2(2)+5\\\\\implies \rm S_2=9\\\\\implies \rm a_1+a_2=9\\\\\implies \rm 7+a_2=9\\\\\implies \rm a_2=2\\\\\rm S_3=2(3)+5\\\\\implies \rm S_3=11\\\\\implies \rm a_1+a_2+a_3=11\\\\\implies \rm 7+2+a_3=11\\\\\implies \rm a_3=2

    \rm We\ get\ a_1=7,a_2=2,a_3=2\\\\\rm From\ this\ we\ can\ conclude\ that\ these\ are\ not\ in\ AP.

    More Info

    \bf nth\ term\ of\ Ap\ ,a_n=a+(n-1)d\\\\\bf Sum\ of\ n\ terms\ of\ Ap\ , S_n=\dfrac{n}{2}[2a+(n-1)d]

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