Here, a = 1; r = 31 = 3; The sum of the first n terms does not exceed 365, i.e.,
Sn ≤ 365.
Now, Sn = r-i
Putting a = 1; r = 3.
Sn = \(\frac{1[3_n−1]}{3−1}\)
Sn = \(\frac{3^n−1}{2}\)
Now, Sn ≤ 365
∴ \(\frac{3^n−1}{2}\) ≤ 365
∴3n – 1≤ 365 × 2
∴ 3n ≤ 730 + 1
∴ 3n ≤ 731
We now tabulate values of 3’ for different positive values of n as shown in the following table and we shall take the maximum value of n for which 3n ≤ 731.
For n = 7, 3n = 2187 which is more than 731.
∴ n = 6 is the maximum value of n, for which 3n ≤ 731.