Question

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

Answer 1

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

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

Answer 2

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 ,

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

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