Question

The sum S of n successive odd numbers starting from 3 is given by the relation : S = n (n + 2). Determine n, if the sum is 168.

Answer 1

we are given, S= n(n+2)

also sum= 168

so,

168= n(n+2)

168= n² + 2n

n²+ 2n - 168 = 0

n² +14n - 12n - 168= 0

n(n +14) -12(n +14)= 0

(n+14) (n-12) =0

.^.. n= 12 or -14

since, n indicates natural number

so, -14 as the value of n is invalid here

.^.. n= 12