Find sum of geometric series 2+6+18+...+1458

planhetkk

planhetkk

Answered question

2022-09-01

Find sum of geometric series 2+6+18+...+1458

Answer & Explanation

Nolan Tyler

Nolan Tyler

Beginner2022-09-02Added 9 answers

Given that first term a 1 = 2 
Common ratio q = a 2 a 1 = 6 2 = 3 
General expression for nth term is
a n = a 1  q n - 1 
Put the above equation's last term's value in to find its number
1458 = 2  3 n - 1 
 3 n - 1 = 1458 2 = 729 
When we use 729 as a power of 3, we get
3 n - 1 = 3 6 , comparing the exponents
n−1=6
or n=7
Now, the expression gives the sum of n terms.
S n = a 1 ( 1 - q n ) 1 - q 
S 7 = 2 ( 1 - 3 7 ) 1 - 3 
= 2 ( 1 - 2187 ) - 2 = 2186 

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