Question

The 6th term of a GP is 1215.given that the common ratio is 3. Find the sum of the 9th term

Answer 1

Answer:

The sum of the 9th term is 1,300.

Step-by-step explanation:

Let A be the first term and r be the common ration of the sequence.

Then Ar^2 = 360 and Ar^5 = 1215.

So r^3 = 1215 / 360 = 3.375

r = cube root (3.375) = 1.5

So A = 360/1.5^2 = 360/2.25 = 160.

So the sum of the first four terms = 160 * (1.5^4 -1)/(1.5–1)

= 320 * (1.5^4 -1) = 1,300.

Answer 2

Answer:

ar^5=1215

r=3

a(3)^5=1215

243a=1215

a=5

ar^8=5(3)^8

=5×6561

=32805

Therefore the 9th term of the G.P is 32805.