Sequences and S...

$$\displaystyle \frac{1}{3^{2}-1}+\frac{1}{5^{2}-1}+\frac{1}{7^{2}-1}+......+\frac{1}{35^{2}-1}=$$

Find the sum of first three terms of the following sequence whose $$n^{th}$$ term is $$5n^2-2$$.

Find the sum of 100 terms of the series $$1(3)+3(5)+5(7)+\cdots\cdots$$

Find the sum of odd numbers between $$2$$ and $$76$$.

Find the next number of the series.
$$7, 10, 8, 11, 9, 12,....$$

Which pair of numbers comes next?
$$25, 23, 5, 20, 16, 5,....$$

Complete the pattern: $$3, 5, 8, 13,$$ ___ 

Look at this series: $$32, 31, 33, 32, 34, 33,...$$. What is the next number?

In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number .If the first number is -5, how many of the numbers in the sequence are positive? 

Which pair of numbers comes next?
$$10, 18, 12, 21, 15 ,25, ,....$$