The minimum number of terms from the beginning of  the series 20+2223+2513+…so that the sum may exceed 1568, is

It is in A.P. for which a=20,d=223=83Now, Sn>1568⇒    n240+(n−1)83>1568⇒    n2×112+8n3>1568⇒    n2+14n>68×1568=1176⇒    n2+14n−1176>0 or     (n+42)(n−28)>0As n is positive, n – 28 > 0 i.e., n > 28 ∴Minimum value of n = 29.