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

n 5 7

an 176 704

Hint: an = a1 (r) n - 1, where a1 is the first term and r is the common ratio.

A. a1 = - 4

B. a1 = 11

C. a1 = 35

D. a1 = - 11

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