If the first term of an arithmetic sequence is 5 and the common difference is 3,

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Question: If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term? (2023)

Options:

Correct Answer: 32

Exam Year: 2023

Solution:

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

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term? (2023)

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term? (2023)

Step 1: Identify the first term (a) of the arithmetic sequence, which is given as 5.
Step 2: Identify the common difference (d) of the arithmetic sequence, which is given as 3.
Step 3: Identify the term number (n) we want to find, which is the 10th term, so n = 10.
Step 4: Use the formula for the nth term of an arithmetic sequence: nth term = a + (n - 1) * d.
Step 5: Substitute the values into the formula: 10th term = 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: Therefore, the 10th term of the arithmetic sequence is 32.

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