The infinite sequence a_{1}, a_{2}, , a_{n}, is such that a_{1} = 7, a_{2} = 8, a_{3} = 10, and a_n=a_{n-3} + 7 for values of n > 3. What is the remainder when a_{n} is divided by 7?
a_{1} = 7
a_{2} = 8
a_{3} = 10
a_{4} = a_1+7=7+7=14
a_{5} = a_2+7=8+7=15
a_{6} = a_3+7=10+7=17
...
Notice that the remainder upon division the above terms by 7 repeats in blocks of 3: {0, 1, 3} {0, 1, 3}...
(1) n is a multiple of 3 --> every third term has the remainder of 3 (a_{3}, a_{6}, a_{9}, ...). Sufficient.
(2) n is an even number. Not sufficient: consider a_2 and a_4.
Answer: A.
a_{1} = 7
a_{2} = 8
a_{3} = 10
a_{4} = a_1+7=7+7=14
a_{5} = a_2+7=8+7=15
a_{6} = a_3+7=10+7=17
...
Notice that the remainder upon division the above terms by 7 repeats in blocks of 3: {0, 1, 3} {0, 1, 3}...
(1) n is a multiple of 3 --> every third term has the remainder of 3 (a_{3}, a_{6}, a_{9}, ...). Sufficient.
(2) n is an even number. Not sufficient: consider a_2 and a_4.
Answer: A.