Define the sequence of positive integers a_n recursively by a_1=3 and a_n=3(a_n- 1) for all n> =2. Determine the last two digits of a_{2007}.
+23252 The first term is 3; each succeeding term is 3 times the preceding term.
Using a calculator and writing down only the last two digits:
a1 = 03 a5 = 43 a9 = 83 a13 = 23 a17 = 63 a21 = 03 a25 = 43 .....
a2 = 09 a6 = 29 a10 = 49 a14 = 69 a18 = 89 a22 = 09 a26 = 29 .....
a3 = 27 a7 = 87 a11 = 47 a15 = 07 s19 = 67 a23 = 27 a27 = 87 .....
a4 = 81 a8 = 61 a12 = 41 a16 = 21 a20 = 01 a24 = 81 a28 = 61 .....
Can you figure out where a2007 belongs in this list?
