Question

The number of terms in the expansion of \( (x + a)^{n} \) is:

• A. $n$
• B. $n+1$
• C. $n-1$
• D. $2n$

Hint:

For $(x+y+z)^{n}$, the number of terms is $(n+1)(n+2)/2$.

Answer 1

The Correct Option is B

Step 1: Concept
According to the Binomial Theorem, $(x+a)^{n} = \sum_{r=0}^{n} {}^{n}C_{r} x^{n-r} a^{r}$.
Step 2: Analysis
The index $r$ starts from 0 and goes up to $n$.
Step 3: Conclusion
The total number of values for $r$ is $n - 0 + 1 = n+1$.
Final Answer: (B)