What is the 10th term of the arithmetic sequence where the first term is 5 and t

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Question: What is the 10th term of the arithmetic sequence where the first term is 5 and the common difference is 3?

Options:

Correct Answer: 35

Solution:

The nth term of an arithmetic sequence is given by a_n = a + (n-1)d. Here, a = 5, d = 3, n = 10. So, a_10 = 5 + (10-1) * 3 = 5 + 27 = 32.

What is the 10th term of the arithmetic sequence where the first term is 5 and the common difference is 3?

What is the 10th term of the arithmetic sequence where the first term is 5 and the common difference is 3?

Step 1: Identify the first term of the sequence, which is given as 5.
Step 2: Identify the common difference of the sequence, which is given as 3.
Step 3: Identify the term number we want to find, which is the 10th term (n = 10).
Step 4: Use the formula for the nth term of an arithmetic sequence: a_n = a + (n-1)d.
Step 5: Substitute the values into the formula: a_10 = 5 + (10-1) * 3.
Step 6: Calculate (10-1) which equals 9.
Step 7: Multiply 9 by the common difference (3): 9 * 3 = 27.
Step 8: Add this result to the first term: 5 + 27 = 32.
Step 9: Conclude that the 10th term of the sequence is 32.

Arithmetic Sequence – An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.
Nth Term Formula – The nth term of an arithmetic sequence can be calculated using the formula a_n = a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number.