For each given geometric sequence, find the sum of the first:
1. 5 terms of 1/2 , 2/3 , 8/9,...
2. 8 terms of 0.2 , 0.02 ,
0.002,...
3. 6 terms of 1/2 , 1/4 , 1/8,...
4. 5 terms of 5/2 , 15/2 ,
45/2,...
5. 7 terms of 0.25 , 1 , 4 , 16,...
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FIND THE GEOMETRIC SEQUENCE
Before we answer this, let's talk about Geometric Sequence, What is Geometric Sequence?
A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. So 1, 2, 4, 8, 16,... is geometric, because each step multiplies by two; and 81, 27, 9, 3, 1, 31 ,... is geometric, because each step divides by 3.
Now you now what is Geometric Sequence, now let's answer!
FIND THE SUM
1. 5 terms of 1/2, 2/3, 8/9
Therefore the next five terms is 9/10, 10/11, 15/16, 16/17 and 17/18.
2. 8 terms of 0.2, 0.02, 0.002
Therefore the next eighth terms is 0.0002(this is hundred thousands), 0.00002(millions), 0.000002(ten millions), 0.0000002(hundred millions), 0.00000002(billions), 0.000000002(ten billions), 0.0000000002(hundred billions), 0.00000000002(trillions).
3. 6 terms of 1/2, 1/4, 1/8
Therefore the next sixth terms is 1/10 or 1, 1/12, 1/14, 1/16, 1/18, and 1/21.
4. 5 terms of 5/2, 15/2, 45/2
Therefore the next five terms is 55/2, 85/2, 95/2, 115/2 and 125/2.
5. 7 terms of 0.25, 1, 4, 16
Therefore the next seventh terms is 19, 31, 34, 46, 49, 61, 64, 76.
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