Mathematics. Geometric sequences.
posted by Olivia .
2+4+8+...is a geometric sequence. Prove the sum of the first n terms is two less than the (n+1)the term.

a = 2 , r = 2
sum(n) = 2(2^n  1)/(21) = 2(2^n  1)
= 2^(n+1)  2
sum(n+1) = 2(2^(n+1)  1)/1 = 2(2^(n+1)  1)
= 2^(n+2)  2
sum(N+1)  sum(n) =2^(n+2)  2  (2^(n+1)  2)
= 2^(n+2)  2^(n+1)
= 2^(n+1) (2  1)
= 2^(n+1) , which is a positive number
so sum(n) < sum(n+1)
Respond to this Question
Similar Questions

Math *URGENT
Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646? 
Maths
An arithmetic and a geometric sequence have the same first terms.(2)....and the same second term say X..The sum of the first 3 terms of the arithmetic sequence equals to the third term of the geometric sequence.Calculate the first … 
Maths
Eric thinks of 2 sequences.One is geometric and the other arithmetic.Both sequences start with the number 3.The common ratio of the geometric sequence is the same as the common difference of the arithmetic sequence.If the 6th term … 
Maths
1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is … 
Maths
Consider all 3term geometric sequences with first term 1 and with common ratio the square of an integer between 1 and 1000. How many of these 1000 geometric sequences have the property that the sum of the 3 terms is prime? 
algebra
Consider all 3term geometric sequences with first term 1 and with common ratio the square of an integer between 1 and 1000. How many of these 1000 geometric sequences have the property that the sum of the 3 terms is prime? 
Math
Consider all 3term geometric sequences with first term 1 and with common ratio the square of an integer between 1 and 1000 (inclusive). How many of these 1000 geometric sequences have the property that the sum of the 3 terms is prime? 
math
in an arithmetic sequence the common difference is equal to 2.the first term is also the first term of a geometric sequence. the sum of the first 3 terms of an arithmetic sequence and the sum of the first 9 terms of an arithmetic sequence … 
Math Help!!!
determine whether each sequence is arithmetic or geometric. find the next three terms. 1. 14,19,24,29.... geometric, 34,39,44 arithmetic,32,36,41 arithmetic 34,39,44**** the sequence is nether geometric nor arithmetic 2. 4,8,16,32.... … 
math
The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric sequence.