A geometric series has second term $6$ and ratio of the seventh term to the sixth term is $3$. What does this question really means?

Question

A geometric series has second term 6 and ratio of the seventh term to the sixth term is $3$. What does this question really means? Sorry I just couldn't get this question. $t(2)=6,$ $6=ar$ from my interpretation is the question saying $t(7) : t(6) = 3$?? what does this means and how do I proceed solving for $a$ and $r$?

Answer 1

If the ratio between the $6^{th}$ and $7^{th}$ terms is $3$, then your common ratio will be $r=3$. You can use this and the second term to find the first term ($t_2 = rt_1$).