Answer: we have that
[3/2,3/8,3/32,3/128,3/512]
the sum of the geometric sequence is [3/2+3/8+3/32+3/128+3/512]
=(1/512)*[256*3+64*3+16*3+4*3]
=(3/512)*[256+64+16+4]
=(3/512)*[340]
=(1020/512)
=255/128---------> 1.9922
the answer is
1.9922
another way to calculate it
is through the following formula
∑=ao*[(1-r^n)/(1-r)]
where
ao---------> is the first term
r----------> is the common ratio between terms
n----------> is the number of terms
ao=1.5
r=1/4-----> 0.25
n=5
so
∑=1.5*[(1-0.25^5)/(1-0.25)]-------------> 1.99
Step-by-step explanation: we have that
[3/2,3/8,3/32,3/128,3/512]
the sum of the geometric sequence is [3/2+3/8+3/32+3/128+3/512]
=(1/512)*[256*3+64*3+16*3+4*3]
=(3/512)*[256+64+16+4]
=(3/512)*[340]
=(1020/512)
=255/128---------> 1.9922
the answer is
1.9922
another way to calculate it
is through the following formula
∑=ao*[(1-r^n)/(1-r)]
where
ao---------> is the first term
r----------> is the common ratio between terms
n----------> is the number of terms
ao=1.5
r=1/4-----> 0.25
n=5
so
∑=1.5*[(1-0.25^5)/(1-0.25)]-------------> 1.99