If the sum of n terms of the sequence 2, 5, 8 | vedclass

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(C) Given the arithmetic progression with first term $a = 2$ and common difference $d = 5 - 2 = 3$. The sum of $n$ terms is given by $S_n = \frac{n}{2

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(C) Given the arithmetic progression with first term $a = 2$ and common difference $d = 5 - 2 = 3$. The sum of $n$ terms is given by $S_n = \frac{n}{2}[2a + (n - 1)d]$. Substituting the values: $60100 = \frac{n}{2}[2(2) + (n - 1)3]$. $120200 = n[4 + 3n - 3]$. $120200 = n(3n + 1)$. $3n^2 + n - 120200 = 0$. Solving the quadratic equation using the quadratic formula $n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$: $n = \frac{-1 \pm \sqrt{1^2 - 4(3)(-120200)}}{2(3)} = \frac{-1 \pm \sqrt{1 + 1442400}}{6} = \frac{-1 \pm \sqrt{1442401}}{6} = \frac{-1 \pm 1201}{6}$. Since $n > 0$,we take $n = \frac{1200}{6} = 200$.

If the sum of $n$ terms of the sequence $2, 5, 8, 11, \dots$ is $60100$,then $n = \dots$

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