Current location - Training Enrollment Network - Mathematics courses - Legend has it that mathematicians of Pythagoras school in ancient Greece often draw dots on the beach or use pebbles to represent numbers. They studied the number of triangles, as shown in the figure:
Legend has it that mathematicians of Pythagoras school in ancient Greece often draw dots on the beach or use pebbles to represent numbers. They studied the number of triangles, as shown in the figure:
(1) From the conditions, an+ 1=an+(n+ 1), so an = (an-an-1)+(an-1-an-2)+…+(A2-A65433).

So the numbers of the triangle are 1, 3, 6, 10,1,28, 36, 45, 55, 66, 78, 9 1,/kloc-0.

So knowing that the number of triangles divisible by 5 appears twice in every five numbers, that is, every five numbers are divided into a group, then the last two numbers of the group can be divisible by 5.

Since b20 14 is a number divisible by 5 of 20 14,

Therefore, it appears in the last number of the 1007 group grouped by five segments in the series {an}.

Therefore, b20 14 is the number in the sequence {an} 1007×5=5035.

(2) Since 2k- 1 is an odd number, it can be known from (1) that the number 2k- 1 divisible by 5 appears in the penultimate position of the K group, so it is the term of k×5- 1=5k- 1 in the sequence {an}, so B2B. 1)2

So the answer is: 5035,5k (5k? 1)2