What are the next two terms in the sequence 1,-3,6,-10,15,-21,

28, - 36

Step-by-step explanation:

We are given a sequence of 1, - 3, 6, - 10, 15, - 21, ...

Now, the difference of 2nd and 1st term is ( - 3 - 1) = - 4 = - 2²

Again, the difference of 3rd and 2nd term is [6 - (-3) ] = 9 = 3²

Now, the difference of 4th and 3rd term is [ - 10 - 6] = - 16 = - 4²

Again, the difference of 5th and 4th term is [15 - (-10) ] = 25 = 5²

Now, the difference of 6th and 5th terms is [ - 21 - 15] = - 36 = - 6²

Therefore, the difference of the terms are - 2², 3², - 4², 5², - 6², ...

From this sequence, it is clear that the next two differences will be 7² i. e 49 and - 8² i. e. - 64

Therefore, the next two terms of the original sequence will be ( - 21 + 49) = 28 and (28 - 64) = - 36. (Answer)