Discussion
How many terms are there in the series 201, 208, 215, ..... 369 ?
Answer: A
The series has 25 terms.
201, 208, 215, ... is an arithmetic progression with first term 201 and common difference 7. If 369 is the \(n\)th term:
\[ \begin{aligned} T_n &= a + (n-1)d \\ 369 &= 201 + (n-1) \times 7 \\ n - 1 &= 168 \div 7 = 24 \\ n &= 25 \end{aligned} \]
24 is the number of gaps between terms, the answer you get by forgetting to add 1 for the first term. 26 and 23 are off-by-one slips in the other direction.
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