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

1+2+3+4+.......+xx= ((n-8)(n-7))/2(n8)(n7)2

Write xx in terms of nn

2 Answers
Aug 8, 2018

x=n-8x=n8

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.

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