Geometric sequences

In a given geometric sequence gn, g4 = 5 and g6 = 11.25. What is g14/g17?

The answer is 8/27. The book uses the geometric sequence formula... I don't understand why they plug certain numbers in. For example... The formula is an=a1r^(n-1)

How do you know what to put in for a1? The book puts in g4 as "a1."

Quote:

---

Originally Posted by benny92000

In a given geometric sequence gn, g4 = 5 and g6 = 11.25. What is g14/g17?

The answer is 8/27. The book uses the geometric sequence formula... I don't understand why they plug certain numbers in. For example... The formula is an=a1r^(n-1)

How do you know what to put in for a1? The book puts in g4 as "a1."

---

Yes, to simplify things let g4 be the first term so that a1 = 5. Then g6 is the third term. Then 11.25 = 5(r^2) and you then solve for r etc.

an=a1r^(n-1) is the usual general term of a geometric sequence.