Multiple choice

Find the 20th term of the given sequence. 3, 5, 8, 12, ...

  1. 212

  2. 210

  3. 204

  4. 182
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A Correct answer
Explanation

The sequence is 3, 5, 8, 12. The differences are 2, 3, 4, which form an arithmetic progression. The n-th term is 3 + sum(i=1 to n-1 of (i+1)) = 3 + (n-1)(n+2)/2. For n=20, 3 + 19*22/2 = 3 + 209 = 212.

AI explanation

The pattern is formed by adding consecutive integers starting with 2, so the differences are 2, 3, 4, and 5. Continuing these additions, the terms from the fifth to the twentieth are 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, and 212. The twentieth term is 212.

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