The first two terms of a sequence are a1=4 and a2=-2. Let a3 be the third term when the sequence is arithmetic and let b3 be the third term when the sequence is geometric. Find a3+b3

 As

        ;          

Therefore,

Step-by-step explanation:

Considering the first two terms of a sequence

Finding when the sequence is arithmetic

Let be the third term when the sequence is arithmetic.

The common difference = d = -2 - 4 = -6

The n-th term of Arithmetic sequence is:

Putting n = 3 in the n-th term to find   .

Finding when the sequence is geometric

Let be the third term when the sequence is geometric.

The common ratio r is:

The n-th term of a geometric sequence with initial value b and common ratio r is given by

Putting n = 3 in the n-th term to find   .

                                                 ∵  

So,

          ;          

Therefore,