Answer:
The sum of the 12 terms = 265720
Step-by-step 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
