Question

What is the first term of the geometric sequence presented in the table below?

Answer 1

To get the first term of the geometric sequence we proceed as follows;
The formula for the arithmetic sequence is:
an=ar^(n-1)
the 5th term is 176, thus;
176=ar^(5-1)
176=ar^4........i

the 7th term is 704, thus;
704=ar^(7-1)
704=ar^6........ii
from i
a=176/r^4
from ii
a=704/r^6
hence;
176/r^4=704/r^6
cross-multiplying the expression we get;
176r^6=--704r^4
dividing both sides by 176r^4 we get:
r^2=4
thus
r=sqrt4
r=2
therefore the first term will be:
a=176/r^4
a=176/2^4
a=11