1. The sequence 9, 18, 27, 36, 45, 54, … consists of successive multiples of 9. This sequence is then altered by multiplying every other term by –1, starting with the first term, to produce the new sequence –9, 18, – 27, 36, – 45, 54,... . If the sum of the first n terms of this new sequence is 180, determine n.

2. In a sumac sequence, t1, t2 , t3 ,…,tm, each term is an integer greater than or equal to 0. Also, each term, starting with the third, is the difference of the preceding two terms (that is, tn+2= tn – tn-1 1 for n ≥ 1 ). The sequence terminates at tm if tm-1- tm < 0 if .

For example:

120, 71, 49, 22, 27 is a sumac sequence of length 5.

Find the positive integer B so that the sumac sequence 150, B, . . . has the maximum possible number of terms.