In the finite sequence of positive integers \(k_1, k_2,\)

[BTGmoderatorLU]

Source: GMAT Prep

I the finite sequence of positive integers \(k_1, k_2, k_3, . . . , k_9\) each term after the second is the sum of the two terms immediately preceding it. if \(k_5=18\), what is the value of \(k_9\)?

1) \(k_4=11\)
2) \(k_6=29\)

The OA is D

[Ian Stewart]

Since we add two consecutive terms to find the next term, once we know two consecutive terms, it is easy to work out every subsequent term in the sequence (and every earlier term, though we don't need to do that here). Using Statement 1, we know the 4th and 5th terms are 11 and 18, so the next is 29, the next is 47, the next is 76 and so on. So we can certainly find k_9 or k_93 or any other later term. The same is true using Statement 2 so the answer is D.