Sequences and S...

Sum the following series to n terms: $$1+3+6+10+15+...$$

Find the sum of the following series to n terms:
$$1\times 2+2\times 3+3\times 4+4\times 5+...$$

Find the sum of the following series to n terms:
$$1+(1+2)+(1+2+3)+(1+2+3+4)+...$$

The next number in the pattern 62, 37, 12 ____ is

If AM of two numbers a and 17 is 15. Then a is ___

Arithmetic mean of two numbers a+d and a-d is 

Find the sum of Arithmetic means of $$3 , 9$$ and $$12 , 8$$.

Insert an arithmetic mean between $$7$$ and $$21$$

The arithmetic mean of $$4$$ and $$14$$ is 

Sum of the series $$S=1^2-2^2+3^2-4^2+.....-2002^2+2003^2$$ is