If the first four terms of an arithmetic sequence are `a,2a,b` and `(a-6-b)` for some numbers a and b, find the sum of the first 100 terms of the sequence.

Explanation

First four terms of an AP are a, 2a ,b and (a-6-b)
So ` " " 2a - a=a-6-b-b`
` rArr " " a= a-6-2b `
`rArr " " - 2b =6rArr b=-3 `
` and " " 2a-a = b -2a `
` rArr " " b= 3a rArr a=-1 `
` therefore ` First terms ` a=-1 and d=a-1 `
` S_(100) =(100)/( 2) [2a +(100-1)d]`
` " "= 50[-2+99(-1) ]`
` " " 50 (-2-99)= 50)(-101)=- 5050`.