Question

How many terms of the sequence 6, 8, 10 ........... must be taken in order that the sum may be
500?

Answer 1

Hey Friend..

Here is the Solution..

The series is : 6, 8, 10, 12.......

Sum of n terms of this series = Sn = 500

⇒ Sn = 500

⇒ $\frac{n}{2}[2a+(n-1)d]$ = 500

⇒ $\frac{n}{2}[2*6+(n-1)2]=500\\\\\frac{n}{2}[12+2n-2]=500\\\\n[6+n-1]=500\\\\6n+n^2-n=500\\\\n^2+5n=500\\\\n^2+5n-500=0\\\\n^2+25n-20n-500=0\\\\n(n+25)-20(n+25)=0\\\\(n+25)(n-20)=0$

∴ n + 25 = 0    or    n - 20 = 0

∴ n = -25 or n = 20

∵ Value of n can't be negative,

∴ Ans. n = 20

${\boxed{Ans,\:n = 20\; i.e.\: 20\: numbers}}$

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I Hope This Will Help You