This is the 9th question in my assignment. It's another confusing question.
Here's the question:
In a geometric progression, the sum of the 2nd and 3rd terms is 12, and the sum of the 3rd and 4th term is 60. Find the common ratio of the first term.
Here's what I did:
I stopped there.
Best Answer
You correctly found that \begin{alignat*}{3} ar & + & ar^2 & = 12 \tag{1}\\ ar^2 & + & ar^3 & = 60 \tag{2} \end{alignat*} If we multiply equation 1 by $r$ and subtract it from equation 2, we obtain $$0 = 60 - 12r \tag{3}$$ Solving equation 3 for $r$ yields the value $r = 5$. If you also need to find the value of the initial term, substitute $5$ for $r$ in equation 1, then solve for $a$.