When a(n)= 145, n= 10.

When n is equal to the fraction, a(n)= 134. But n can only be a positive integer, so a(n) can't be equal to 134.

Group the pebbles in the picture as shown.

1+(3 * 1+ 1)+(3 * 2+ 1)+(3 * 3+ 1)+…+3 *(n- 1)+ 1 = 3n(n- 1)/2+n