Question

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

Answer 1

The sum of terms 12 the geometric sequence 1,3,9... = 265720

Explanation:

Formula:-

Sₙ = a₁(1 - rⁿ)/(1 - r)

Where Sₙ - sum of n terms in the GP

a - First term of GP

r - Common ratio

n - Number

It is given the geometric sequence 1,3,9....

To find the sum of 12 terms

Here a = 1, r = 3 and n = 12

Sₙ = a₁(1 - rⁿ)/(1 - r) = 1(1 - 3¹²)/(1- 3) = 265720

Answer 2

The sum of the 12 terms = 265720

Explanation:

* Lets study the geometric sequence rule

- If a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , .........................

∴ an = a[(r)^(n-1)]

- Where a is the first term and r is the common ratio and

n is the position of the term in the sequence

- The rule of the sum of some terms is Sn = [a(1 - r^n)]/(1 - r)

- Where n is the number of terms we want to add

* Lets check our terms in the sequence

- The terms are 1 , 3 , 9 , ..........

- To find the common ratio divide the 2nd term by 1st term

∵ the second term is 3 and the first term is 1

∴ 3/1 = 3

∴ The common ratio is 3

∵ n = 12 and a = 1

* Lets substitute the values of a , r , n in the rule of the sum to

find the sum of the 12 terms

∴ S12 = [1(1 - 3^12)]/(1 - 3) = (1 - 3^12)/-2 = 265720

* The sum of the 12 terms = 265720