Question:The nth term of a sequence is defined by a_n = 5n - 7. What is the value of a_12?

1. TRANSLATE the problem information

• Given information:
  • Sequence formula: \(\mathrm{a_n = 5n - 7}\)
  • Need to find: \(\mathrm{a_{12}}\)

• What this tells us: We need to substitute \(\mathrm{n = 12}\) into the given formula

2. SIMPLIFY through direct substitution

• Substitute \(\mathrm{n = 12}\) into \(\mathrm{a_n = 5n - 7}\):
  • \(\mathrm{a_{12} = 5(12) - 7}\)
  • \(\mathrm{a_{12} = 60 - 7}\)
  • \(\mathrm{a_{12} = 53}\)

Answer: C. 53

Why Students Usually Falter on This Problem

Most Common Error Path:

Incomplete SIMPLIFY execution: Students correctly substitute but forget to subtract the 7

• They calculate: \(\mathrm{a_{12} = 5(12) = 60}\) and stop there
• This leads them to select Choice D (60)

Second Most Common Error:

Weak SIMPLIFY skills: Students make arithmetic errors during calculation

• They might misread the subtraction or make computational mistakes
• Common errors: \(\mathrm{60 - 7 = 48}\) (confusing with \(\mathrm{60 - 12}\)) or other arithmetic slips
• This may lead them to select Choice B (48) or cause confusion and guessing

The Bottom Line:

This problem tests whether students can accurately perform function evaluation - the key challenge isn't understanding what to do, but executing the arithmetic correctly without dropping steps or making computational errors.