Find the sum of the first 6 terms of a geometric sequence for which a1 = 2 and r = 3. Sum ?

Answer 1

Since our ratio is 3, we calculate the first 6 terms starting with a_1.Doing this by hand should look like:

a₁ = 2

a₂ = 2*3 = 6

a₃ = 6*3 = 18

a₄ = 18*3 = 54

a₅ = 54*3 = 162

a₆ = 162*3 = 486

Simply add each term for your answer. However, I recommend using the summation equation for finite geometric series. The equation is:

S_n = a₁(1-rⁿ)/(1-r)

where a₁ is the initial term, r is the common multiple (3 in this case), and n is the number of terms. They ask for a₆ so our n = 6. Plugging these values in should yield

S_n = 728