What is the sum of the geometric sequence 1, 3, 9, ... if there are 14 terms?

Solution:

Given: Geometric sequence is 1, 3, 9, ...14 terms

Sum of the geometric sequence S = a + 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 = 14

S₁₄ = 1 (3¹⁴ - 1) / (3 - 1)

S₁₄ = (4782969 - 1) / 2

S₁₄ = 4782968 / 2

S₁₄ = 2391484

Therefore , the sum is 2391484.

---

What is the sum of the geometric sequence 1, 3, 9, ... if there are 14 terms?

Summary:

The sum of the geometric sequence 1, 3, 9, ... if there are 14 terms is 2391484.