Question

Find the 6th term in this series: {1, 15, 45, 135, ...} *

Answer 1

Alright, since after the second term, the pattern is consistent, we will be using the 3rd and 2nd terms in the formula, instead of the 2nd and 1st.
1. divide the 3rd term by the second term. 45/15=3
2. Check the pattern by applying this method to the 4th and 3rd terms. 135/45=3 This means is is in fact G.S.
3. Now we go back to the traditional formula, which would be 1st term*r^n-1
4. Work it out. The r in the formula represents the 3, which we worked out. The n in the formula represents the term your trying to find. 15*3^6-1=3645
Your answer for the 6th term should indeed be 3645, which may sound odd, but it's right.
~Hope this helps!