Question

In a geometric progression, the sum of the 2rd and 3rd is 12 and sum of the 3rd and 4th is 60. Find the common ratio and the first term.​

Answer 1

Answer:

You correctly found that

arar2++ar2ar3=12=60(1)(2)

If we multiply equation 1 by r and subtract it from equation 2, we obtain

0=60−12r(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.