To find the 64th term of the arithmetic sequence, we will use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where:
- a_n is the nth term we want to find,
- a_1 is the first term of the sequence,
- d is the common difference between the terms,
- n is the term number.
Let's calculate the values we need:
1. The first term of the sequence (a_1) is given as 29.
2. To find the common difference (d), we subtract the first term from the second term:
d = 38 - 29 = 9
3. The term number (n) we want to find is the 64th term, so n = 64.
Now that we have all the necessary values, we can plug them into the formula to find the 64th term.
a_64 = 29 + (64 - 1) * 9
a_64 = 29 + 63 * 9
a_64 = 29 + 567
a_64 = 596
So the 64th term of the sequence is 596.
