What is the sum of the geometric sequence 1, 3, 9, ... if there are 12 terms?

Solution:

Sum of the geometric sequence is :

S = a + ar + ar¹ + ar² +....+ ar^{n - 1}

First term of the series a is 1.

Common ratio  is r.

To find r,

r = 3/1

r = 3

Since r > 1, sum of geometric sequence can be found by using the relation,

S_n = a(rⁿ - 1)/(r - 1), r ≠ 1

Given, n = 12

S₁₄ = 1 (3¹² - 1)/(3 - 1)

S₁₄ = (531441 - 1)/2

S₁₄ = 531440/2

S₁₄ = 265720

Therefore, the sum of the geometric sequence is 265720.

---

What is the sum of the geometric sequence 1, 3, 9, ... if there are 12 terms?

Summary:

The sum of the geometric sequence 1, 3, 9, ... if there are 12 terms is 265720.