If AM and GM satisfy the equation 4x2−9x+5=0, then AM and GM are nothing but roots of this quadratic equation, 4x2−9x+5=0 ⇒4x2−4x−5x+5=0 ⇒4x(x−1)−5(x−1)=0 ⇒(x−1)(4x−5)=0 ⇒x=1,
5
4
Then, AM =
5
4
and GM=1[∵AM≥GM] Again, the given series is −16,8,−4,2..... which is a geometric progression series with common ratio