To find the tenth term of the expansion of (x + 2y)^16, which value of r goes into the formula for the (r + 1)th term?

1. The formula gives the (r + 1)th term rather than the rth term, so the index is shifted by one. 2. The tenth term means r + 1 = 10. 3. Subtracting 1 from both sides gives r = 9. 4. The general term is then the coefficient 16 over 9 multiplied by x to the power 16 - 9 and by (2y) to the power 9. 5. Using r = 10 would return the eleventh term, which is the off-by-one trap this formula sets. 6. The value 16 is the outer exponent n, not the position index, so it never plays the role of r. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.6 Binomial Theorem_