Multiple choice

Find the 19th term of the given squence. 10, 14, 19, 25...

  1. 235

  2. 236

  3. 248

  4. 259
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A Correct answer
Explanation

nth term = a + (n – 1)d + ${\frac 12}$ (n – 1) (n – 2) c a = 10, d = 4, c = 1, n = 19               = 10 + (19 – 1) 4 + ${\frac 12}(19-1)(19-2)$1              = 10 + 18 $\times$ 4 + 9 $\times$ 17              = 235

AI explanation

The differences between consecutive terms (4, 5, 6, 7...) increase by 1 each time, so this isn't a simple AP but a sequence where the kth gap equals k+3. Summing these gaps up to the 19th term (10 + Σ from k=1 to 18 of (k+3)) gives 10 + 171 + 54 = 235. This method of summing successive differences is the standard way to extend such quadratic-type sequences.

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