In the expansion of (a + b)ⁿ

     Total number of terms = index count + 1

=> Total number of terms = n + 1                {Here index count = n}

1. Example: Find the total number of terms in the expansion of (a + b)ⁿ 

     Total number of terms = index count + 1

=> Total number of terms = 2 + 1 = 3                {Here index count = 2}

2. Again, 

      (a + b)³ = ³C₀ a³ * b⁰ + ³C₁ a^3-1 * b⁰⁺¹ + ³C₂ a^3-1 * b⁰⁺² + ³C₃ a^3-3 * b⁰⁺³ +

=> (a + b)³ = ³C₀ a³ * b⁰ + ³C₁ a² * b¹ + ³C₂ a¹ * b² + ³C₃ a⁰ * b³ 

So, the power of the first quantity a goes on decreasing by 1 whereas the powers of the second quantity b increase by 1 in the successive terms.

3. Again, in each term of the expansion, the sum of the indices of a and b is the same and is equal to the index of (a + b).

Now, in (a + b)³ , the index = 3

In the first term, a has index 3 and b has index 0

Now a + b = 3 + 0 = 3 which is equal to the index of (a + b)³

Again, a + b = 3 for rest of the terms.  

Hope you got the point.