Question
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.
Answers
GPT 3.5
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.
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.
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
10th_term = 3 1/2 + 9 * (2 1/3)
= 3 1/2 + 18 9/3
= 3 1/2 + 21
= 24 1/2
GPT 3.5
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.
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.
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