Question

can you please help me with this.

Answer 1

Answer:

Step-by-step 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

$a_{13}=38$

Answer 2

Answer:

38

Step-by-step 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.