दर्शाइए की a_(1), a_(2), …… a_(n),…… से एकA.P. बनती हैं, यदि a_(n) नीचे दिए अनुसार परिभाषित हैं ...

If a_(1),a_(2),...,a_(n) be an A.P. of positive terms, then

Find a_(1) and a_(9) if a_(n) is given by a_(n) = (n^(2))/(n+1)

STATEMENT-1 : If a, b, c are in A.P. , b, c, a are in G.P. then c, a, b are in H.P. STATEMENT-2 : If a_(1) , a_(2) a_(3) ……..a_(100) are in A.P. and a_(3) + a_(98) = 50 " then" a _(1) + a_(2) +a_(3) + ….+ a_(100) = 2500 STATEMENT-3 : If a_(1) , a_(2) , ....... ,a_(n) ne 0 then (a_(1) + a_(2)+ a_(3) + .......+ a_(n))/(n) ge (a_(1) a_(2) .........a_(n) )^(1//n)

The fibonacct sequence is defined by 1=a_(1) = a_(2) and a_(n-1) + a_( n-1) , n gt 1 Find (a_(n+1))/(a_(n)) " for " n =1 ,2,34,5,