Question

A G.P is such that 3rd term is 9times the first term, while the 2nd term is one twenty fourth of the 5th term. Find its 4th term

Answer 1

Answer:

I’m afraid those conditions are incompatible. A Geometric Progression (GP) is simply a series of terms where each term after the 1st term is obtained by multiplying the previous term by some constant, p, the common ratio. If we call your 1st term a, the 2nd term will be p x a, the 3rd term will be p x p x a, etc. The n’th term can be written as a(sub n) = p^(n-1) x a. In your 1st condition, you want that 3rd term to be 9 times the 1st term, so p x p x a = 9 x a or p = 3. So far, so good. However in the 2ndcondition, you want the 5th term to be 24 times the 2nd term, so p^4 x a = 81 x a (if p = 3) would have to = 24 x 3 x a = 72 x a. Since 81 x a can’t = 72 x a, the conditions are incompatible and your problem has no solution.

I suspect you copied the problem incorrectly from some source or made a typo when entering it into Quora. Note that if your 2nd condition had specified that the 2nd term was one-twenty seventh of the 5th term, this would also lead to a common ratio of p = 3. Then, the 4th term in your GP would be 27 times the 1st term (or 9 times the 2nd term or 1/3 of the 5th term.) Hope this all helps you a little.