Multiple choice

Find the nth term of a sequence for which t1 = 0 and tn = tn - 1 + 4 for n > 1.

  1. 4n - 1

  2. 4(n - 1)

  3. n - 4

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is an arithmetic progression where t1 = 0 and the common difference is 4. The formula is t_n = a + (n-1)d = 0 + (n-1)4 = 4(n-1).

AI explanation

The sequence is defined recursively with the first term being 0 and each subsequent term increasing by 4. This means the second term is 0 plus 4, which is 4, the third term is 4 plus 4, which is 8, and the fourth term is 8 plus 4, which is 12. This generates the terms 0, 4, 8, 12, and so on, which forms an arithmetic progression. The general formula for the nth term of an arithmetic progression is tn equals a plus n minus 1 times d, where a is the first term and d is the common difference. Substituting the values, we get tn equals 0 plus n minus 1 times 4, which simplifies to 4(n - 1).

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