Question

find the value of x such that 25+22+19+16+......+x=112

Answer 1

Answer:

As we see it is an AP

first number a= 25 command difference d= 22-25=-3

Using sum formula

S=n/2 (2a+(n-1)d)

112=n/2 (2×25+(n-1)(-3))

112=n/2 (50-3n+3)

224=53n-3nsquare

Solving quadratic

3nsquare+224-53n=0

3nsquare-21n-32n+224=0

3n(n-7)-32(n-7)

(n-7)(3n-32)

n=7 and n= 32/3

Neglecting the second term ,n=7