arithmetic sequences practice

Answer 1

1. Find the common difference in the arithmetic sequence: 2, 5, 8, 11, 14, ...

To find the common difference, subtract each term from the previous term:
5 - 2 = 3
8 - 5 = 3
11 - 8 = 3
14 - 11 = 3

The common difference is 3.

2. Find the 10th term in the arithmetic sequence: 3, 6, 9, 12, 15, ...

To find the 10th term, we need to use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d

Where:
an = the nth term
a1 = the first term
n = the term number
d = the common difference

In this case:
a1 = 3
n = 10
d = 3

Now plug these values into the formula:
a10 = 3 + (10-1) * 3
a10 = 3 + 9 * 3
a10 = 3 + 27
a10 = 30

The 10th term in the sequence is 30.