Question

If you are given the seventh term of a geometric sequence and the common ratio, how can you determine the second term of the sequence without writing an explicit rule or a recursive rule?(fill in the blank) ⬇️ Divide the seventh term by the common ratio ____ times. If given the second term, you would _____ the common ratio ___ times to get the seventh term, so perform the inverse operation.

Answer 1

A geometric sequence is one where to get from one term to the next one you multiply by the same number (called the common ratio) each time.

If we know the seventh term of the geometric sequence and the common ratio, then to find the second term of the sequence, we need to divide the seventh term by the common ratio (n-2) times, the reasoning is n is the term we know and 2 is the term we want to know, then as n=7, we have to divide the seventh term by the common ratio 5 times. If given the second term, you would multiply the common ratio 5 times to get the seventh term, so perform the inverse operation.