Partial Sums of Arithmetic and Geometric Sequences

Question

If a₁ is 8 and r is -2/3, find s₃

 

 

 

Whats the formula for this? The question doesn't leave much for me to go off of.

Answer 1

For a geometric sequence, S_n, the sum of the first n terms, can be found by using the formula:

 

S_n = [a₁(1 - rⁿ)]/(1 - r)

 

So, for the given sequence, S₃ = [8(1  - (-2/3)³]/(1 - (-2/3))

 

                                                      = 8(1+ (8/27))/(5/3)

 

                                                      = 8(35/27)(3/5)

 

                                                      = 56/9