a > 0 and 0" class="fm-inline"> r > 0 . Now, 2 " class="fm-inline"> a n = a n − 1 + a n − 2 , n > 2 ⇒ a r n − 1 = a r n − 2 + a r n − 3 ⇒ r 2 = r + 1 ⇒ r 2 − r − 1 = 0 0] " class="fm-inline"> ⇒ r = 1 ± √ 5 2 ⇒ r = 1 + √ 5 2 [ ∵ r > 0 ]" >
Let a be the first term and r be the common ratio of the G.P. Then, a>0 and r>0. Now, an=an−1+an−2,n>2 ⇒arn−1=arn−2+arn−3 ⇒r2=r+1⇒r2−r−1=0 ⇒r=
