Question

Can you please help me with this.

Answer 1

38

Explanation:

This isn't the most efficient way but it's the best I can do.

2, 5, 8, 11....

The pattern is that we add 3 every time.

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38,

1 , 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

We can see that 38 is the 13th term of the sequence.

Answer 2

Explanation:

The equation for an arithmetic sequence is

`a_n=a_1+d(n-1)` where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the difference between the numbers in the sequence.

Our first number is 2, so a1 = 2; to get from 2 to 5 we add 3, to get from 5 to 8 we add 3. That means that d = 3. Filling in the standard form of the equation:

`a_n=2+3(n-1)` which simplifies to

`a_n=2+3n-3` and a bit more to

`a_n=3n-1` (which should tell you that arithmetic sequences are lines!)

Finding the 13th number simply requires that we replace n with 13 and solve:

`a_(13)=3(13)-1` so

`a_(13)=38`