Multiple choice

If the fifth term of a sequence is 15 and tenth term is 20, find the first term and common difference.

  1. 11, 1

  2. 12, 2

  3. 14, 3

  4. 15, 4
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A Correct answer
Explanation

For an arithmetic sequence, a + 4d = 15 and a + 9d = 20. Subtracting the equations gives 5d = 5, so d = 1. Substituting d = 1 into the first equation, a + 4 = 15, so a = 11.

AI explanation

Using the formula for the nth term of an arithmetic progression, a + 4d = 15 and a + 9d = 20. Subtracting the first equation from the second gives 5d = 5, so the common difference d is 1. Substituting d = 1 into the first equation yields a + 4(1) = 15, which means the first term a is 11. The result is 11, 1.

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