Can someone solve this? IGCSE MATH, SEQUENCES QUESTION Book answer= (n-8)

1+2+3+4+.......+#x#= #((n-8)(n-7))/2#

Write #x# in terms of #n#

2 Answers
Shwetank Mauria
Aug 8, 2018

#x=n-8#

Explanation:

Sum of the series #1+2+3+4+........+x# is #(x(x+1))/2#

and as sum is given as #((n-8)(n-7))/2#

comparing the two we observe that while denominator is same,

in numerator, we have two numbers #x# and #x+1# former being smaller, whose difference is #1#

and same we have in #n-8# and #n-7#

Hence #x=n-8#.

Narad T.
Aug 8, 2018

Please see the explanation below

Explanation:

We know that the sum of natural numbers is

#sum_(k=1)^xk=x/2(x+1)#

But it is given that

#sum_(k=1)^xk=((n-8)(n-7))/2#

Therefore,

#x/2(x+1)=((n-8)(n-7))/2#

For this equation to be true, there is only one solution

#x=n-8#

as

#x+1=n-7#, #=>#, #x=n-8#

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