Question

If 100 more than the sum of n consecutive
natural numbers is equal to the sum of the
next n consecutive natural numbers, find n​

Answer 1

Answer:

Step-by-step explanation:

let us assume the first number to be a

then,

it will be an AP of a,a+1,a+2.....,a+n-1

therefore the starting number of second series will be a+n,

the AP will be a+n,a+n+1,a+n+2....,a+2n-1

the sum of first AP is n(a+a+n-1)/2

the sum of first AP is n(a+n+a+2n-1)/2

hence,

n(2a+n-1)/2+100=n(2a+3n-1)/2

n(2a+n-1)+200=n(2a+3n-1)

and a=1(since natural number)

n(2+n-1)+200=n(2+3n-1)

n(n+1)+200=n(3n+1)

n2+n+200=3n2+n

200=2n2

n2=100

n=10

Answer 2

Answer:

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