1.

Find the value of x if `2+4+6+...+x=650`

Answer» Here, a=2,
`d=4-2=6-4=2`
Let `S_(n)=650`
`rArr (n)/(2)[(2(2)+(n-1)2]=650 rArr n(n+1)=650`
`rArr n^(2) +n-650=0 rArr (n+26)(n-25)=0`
`rArr n=-26 or n=25`
n=-26 is not possible as number of terms cannot be negative.
`:. n=25`
Now, `x=a_(25)=2+24(2)=50`


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