Use the explicit or recursive formulas for the geometric sequence 45, 135, 405, 1215, 3645, ... to find the sum of the first 9 terms of the sequence.

Question

I NEED ASAP PLEASE HELPPPP

Answer 1

for a geometric sequence, find the common ration, r = 3

take any term and divide it by the previous term to find r. 135/45 = 3 = r

an = a1(r)^(n-1)

a1 = 45r^0 = 45

a2 = 45r^1 = 45(3) = 135

a3 = 45(3^2) = 405

a4 = 45(3^3) = 1215

a5 = 45(3^4) = 3645

a6 = 45(3^5) = 10935

a7 = 45(3^6) = 32805

a8 = 45(3^7) = 98415

a9 = 45(3^8) = 295,245

add them up: 442,845

but there's an easier way to solve this problem, using a formula for the sum of n terms of a geometric sequence

sn = a1(r^n-1)/(r-1) for lrl not equal to 1

s9 = 45(3^9 -1)/(3-1) = 45(19683-1)/2 = 885,690/2 = 442,845