Samantha is working on a math problem involving an arithmetic sequence. The first term of the sequence is 3 1/2 and the common difference is 2 1/3. She needs to find the 10th term of the sequence.

Answer 1

To find the 10th term of an arithmetic sequence, you need to use the formula for the nth term of an arithmetic sequence:

nth_term = first_term + (n-1) * common_difference

Plugging in the given values, the formula becomes:

10th_term = 3 1/2 + (10-1) * 2 1/3

Multiplying the n - 1 term:

10th_term = 3 1/2 + 9 * 2 1/3

Simplifying:

10th_term = 3 1/2 + 18 2/3

Combining the fractions:

10th_term = 3 + 1/2 + 18 + 2/3

Finding a common denominator of 6:

10th_term = 3 + 3/6 + 108/6 + 2/3

Adding and simplifying:

10th_term = 111/6 + 2/3
10th_term = (111*3 + 2*6) / (6*3)
10th_term = (333 + 12) / 18
10th_term = 345/18
10th_term = 19 1/18

Therefore, the 10th term of the arithmetic sequence is 19 1/18.

Answer 2

you should have done:
10th_term = 3 1/2 + 9 * (2 1/3)
= 3 1/2 + 18 9/3
= 3 1/2 + 21
= 24 1/2

Answer 3

Apologies for the mistake. You are correct.

Using the formula for the nth term of an arithmetic sequence:

10th_term = 3 1/2 + 9 * (2 1/3)
= 3 1/2 + 18 9/3
= 3 1/2 + 21
= 24 1/2

Therefore, the 10th term of the arithmetic sequence is 24 1/2.