If the sum of the first 2n terms of the A.P. 2,5,8 ... ... n is equal to the sum of the first n terms of the A.P. 57,59 ,n 61, ... ... .. then n equals

(c) : Sum of 2 n terms of 2,5,8 ... ... .. isnn(2 n / 2)[2 x 2+(2 n-1) 3]=n(6 n+1)nnand sum to n terms of 57,59,61, ... ... ... .. isnn=(n / 2)[2 x 57+(n-1) 2]=(n / 2)(2)(57+n-1)=n(56+n)nnnAccording to given conditionnn n n(6 n+1)=n(56+n) n => 6 n+1=56+n n => 5 n=55 => n=11n n

If the sum of the first 2n terms of the A.P. 2,5,8 is... | Sequence & Series (Mathematics)

2 n

terms of

2,5,8 \ldots \ldots .

. is\n

\n\frac{2 n}{2}[2 \times 2+(2 n-1) 3]=n(6 n+1)\n

\nand sum to

n

terms of

57,59,61, \ldots \ldots \ldots .

. is\n

\n=\frac{n}{2}[2 \times 57+(n-1) 2]=\frac{n}{2}(2)(57+n-1)=n(56+n)\n

\n\nAccording to given condition\n

\n\begin{aligned}\n& n(6 n+1)=n(56+n) \\\n& \Rightarrow 6 n+1=56+n \\\n& \Rightarrow 5 n=55 \Rightarrow n=11\n\end{aligned}\n

Explanation

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