When the terms of a geometric sequence are added together, a geometric series is formed.
is a finite geometric sequence.
is a finite geometric series.
The sum of terms, , of a geometric sequence equals:
if or (eg. )
if (eg. )
Find the sum of the first ten terms of the sequence to five decimal places.
As , use the second equation.
The question says that we need to answer to five decimal places so:
The sum of the first ten terms is 0.49999.
The sum can be a positive or a negative number.
The second term of a geometric is 22 and the fifth term is -176. Find the sum of the first eight terms of the sequence correct to one decimal place.
We need to find the value of and .
So far we have this information:
To find , we need to solve these two equations simultaneously.
Now that we have the value of , we can substitute it into either of the equations to find the value of .
We know know each of the values so we can substitute these into the equation. As , use the first equation.
The question asked for the answer correct to one decimal place.
The sum of the first eight terms of the geometric series is -469.3.
Finding the Terms of a Geometric Sequence
Sum of an Infinite Geometric Sequence
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