given:
a1 +a2 + ......an = 350
every term has to be either 7 or 77.

my approach:

350/7 = 50 - all ans choices are less than 50.

so there shd be atleast one term with value 77.
so 1*77 + 39*7 = 350
therefore the total num of terms = 1+39 =40