What is the one hundredth term in the sequence 1 3 6 10 15 21 28?

Answer 1

The sequence given is an arithmetic sequence where each term is the sum of the previous term and a constant difference. The constant difference in this sequence is increasing by 1 each time, starting with 2. To find the 100th term, we can use the formula for the nth term of an arithmetic sequence: ( a_n = a_1 + (n-1)d ), where ( a_n ) is the nth term, ( a_1 ) is the first term, ( n ) is the term number, and ( d ) is the common difference. Plugging in the values, we get ( a_{100} = 1 + (100-1)2 = 1 + 99*2 = 1 + 198 = 199 ). Therefore, the 100th term in the sequence is 199.

Answer 2

These are most probably the triangular numbers and T100 = 100*101/2 = 5050.

Of course, it is possible to find a polynomial of degree 7 (or higher) so that ANY number can be the next term, or the 100th term.