Start by multiplying the sum of the terms by the common ratio.
To write a different sequence use the formula for the sum, S= a_11-r, where a_1 is the first terms and r is the common ratio.
Sum: 2 Example Sequence: a_n=4/3( 1/3)^(n-1)
Practice makes perfect
We will first find the sum of the terms of the geometric sequence.
1, 1/2, 1/4, 1/8, ... 1/2^(n-1), ...
Then we will write another sequence whose sum of the terms is the same as the above sequence.
Sum of Terms
Let S denote the sum of the terms of the geometric sequence.
S=1+ 1/2+ 1/4+ 1/8+ ...Now we will multiply both sides of the equation by the common ratio of the sequence, 12.
We will subtract S2 from S.
S- S/2 =
1 - 1/2
+1/2 - 1/4
+1/4 - 1/8
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... ...
S- S/2 = 1
All terms, except 1, will cancel each other out. Therefore, the right hand-side is equal to 1. We can now find S.
The formula below gives the sum of the terms of a geometric sequence.
S=a_1/1- r
Here, a_1 is the first terms and r is the common ratio. We want S to be 2. Hence, we should find a_1 and r such that a_1/1-r=2. Let say r= 13. Then, a_1 should be 43.
