Answer
$a_9 = 57$
$a_{10} = 64$
Work Step by Step
We can find the ninth and tenth terms by figuring out the explicit formula of a sequence, which will give us the exact term we are looking for.
The pattern in this exercise is that the next term is given by adding $7$ to the previous term. This means that this is an arithmetic sequence because we are adding the same number to the previous term to get the next term.
Use the explicit formula for arithmetic sequences, which is $a_n = a + (n - 1)d$, where $a$ is the first term of the sequence and $d$ is the common difference; in this exercise, $a$ is $1$ and $d$ is $7$:
$a_n = 1 + (n - 1)7$
Substitute $9$ for $n$ to find the $9$th term of the sequence:
$a_9 = 1 + (9 - 1)7$
Evaluate what's in parentheses first:
$a_9 = 1 + (8)7$
Then multiply:
$a_9 = 1 + 56$
Add to solve:
$a_9 = 57$
Substitute $10$ for $n$ to find the $10$th term of the sequence:
$a_{10} = 1 + (10 - 1)7$
Evaluate what's in parentheses first:
$a_{10} = 1 + (9)7$
Then multiply:
$a_{10} = 1 + 63$
Add to solve:
$a_{10} = 64$
