Multiple choice

What of the following numbers is 25 less than the 25th term of the sequence 5, 9, 14, 20, ...?

  1. 352

  2. 377

  3. 394

  4. 382
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A Correct answer
Explanation

The sequence is 5, 9, 14, 20... Differences are 4, 5, 6... This is a quadratic sequence. n-th term = a + (n-1)d1 + (n-1)(n-2)d2/2. Here a=5, d1=4, d2=1. T_n = 5 + 4(n-1) + (n-1)(n-2)/2 = 5 + 4n - 4 + (n^2 - 3n + 2)/2 = (n^2 + 5n + 4)/2. For n=25, T_25 = (625 + 125 + 4)/2 = 754/2 = 377. 25 less than 377 is 352.

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