Finite geometric series
Table of Contents
finite geometric series (EMCDZ)
Finite geometric series grade 12 is When we sum a known number of terms in a geometric sequence, we get a finite geometric series. We generate a geometric sequence using the general form thus make Finite geometric series grade 12
where
 n
 is the position of the sequence;
 Tn
is the nth
 term of the sequence;
 a
 is the first term;
 r
 is the constant ratio.
General formula for a finite geometric series (EMCF2)
The general formula for determining the sum of a geometric series is given by:
This formula is easier to use when r<1
.
Alternative formula:
The general formula for determining the sum of a geometric series is given by:
This formula is easier to use when r>
Worked example 11: Sum of a geometric series
Calculate:
Write down the first three terms of the series
We have generated the series 32+16+8+â‹¯
Determine the values of a
and r
Use the general formula to find the sum of the series
Write the final answer
Worked example 12: Sum of a geometric series
Given a geometric series with T1=âˆ’4
and T4=32. Determine the values of r and n if Sn=84
.
Determine the values of a
and r
Therefore the geometric series is âˆ’4+8âˆ’16+32â€¦
Notice that the signs of the terms alternate because r<0.
We write the general term for this series as Tn=âˆ’4(âˆ’2)nâˆ’1
.
Use the general formula for the sum of a geometric series to determine the value of n
Write the final answer
Worked example 13: Sum of a geometric series
Use the general formula for the sum of a geometric series to determine k
if
Write down the first three terms of the series
We have generated the series 12k+14k+18k+â‹¯
We can take out the common factor k
and write the series as: k(12+14+18+â‹¯)
Determine the values of a
and r
Calculate the sum of the first eight terms of the geometric series
So then we can write:
Write the final answer

Interactive Exercises