Question

Find the sum of a 10-term geometric sequence when the first term is 3 and the last term is 59,049 and select the correct answer below.

177,147
88,572
88,575
177,144

Answer 1

first, find the r.

59049=3r^10-1

59049=3r^9 divide both sides by 3

19683=r^9 9 roots both side

r=3

Next, find the 10 terms.

(3-3(3)^10)/(1-3)

s10=88572

i just took the test and it waS CORRECT.

Explanation:

Answer 2

First, we need to solve for the common ratio from the data given by using the equation.

a(n) = a(1) r^(n-1)
59049 = 3 r^(10-1)
19683 = r^9
r = 3

Then, we can find the sum by the expression:

S(n) = a(1) ( r^n -1) / 1-r
S(10) = 3 (3^10 -1 ) / 3-1
S(10) =88572