alleryHow many terms are in the expansion of $(a + b)^{15}$?
A$15$
B$16$
C$17$
D$120$
Answer & Solution
Correct answer: B. $16$
1. The expansion of $(a + b)^n$ has $n + 1$ terms — one for each value of the index $r = 0, 1, 2, \ldots, n$.
2. For $n = 15$: number of terms $= 15 + 1 = 16$.
3. These correspond to $T_1, T_2, \ldots, T_{16}$.
4. Option A is off by one (forgetting that $r$ starts at 0). Option C is off by two. Option D is incorrect computation.
_Source: syllabus Mathematics, Ch 7, §7.2.1 (General Term — observation), p. 5._
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