To find this we need to find the general term of the sequence, so we need to find a formula that contains “ the n”, where n is a random term form the sequence. What formula may the sequence $\displaystyle \left\{ {2,4,6,8…….\left. . \right\}} \right.$ have.

Firstly we see that the terms of our sequence grow with 2, that´s why we can suggest that the sequence might be something like “2 multiplies n“ where n is the n-th term.

We can test it by trying the first 4-th natural numbers 1,2,3,4 and we get 2n=2⋅1 = 2, 2n=2⋅2 = 4, 2n=2⋅3 = 6 and 2n=2⋅4 =8.In this case it was easy to find out the formula.

Now that we have the general formula $ \displaystyle {{a}_{n}}=2n$ we can solve our questions.

**a)** The 10-th term is $ \displaystyle {{a}_{{10}}}=2\cdot 10=20$

**b)** The 100-th term is $ \displaystyle {{a}_{{100}}}=2\cdot 100=200$

Now, whatever term we want we can find if we have the general formula of the sequence. If we are looking for the 13-th term then $ \displaystyle {{a}_{{13}}}=2\cdot 13=26$.