Answer to Question #150706 in Algebra for Siti Nur Alwani Mohd Anuar Musardar

Question

The fourth term of a geometric sequence exceeds the second term by 150 and the third term is four times the fifth term. Find the first term and common ratio of the sequence by assuming common ratio is positive.

Answer 1

Let us consider that very first five terms of given GP series are....

$$a,ae,ae^2,ae^3,ae^4$$

where "e" is the common ratio.

Now according to the question...

$$ae^3 = ae+150....Eq[1]\\ \&\\ ae^2=4\times ae^4\\ \Rightarrow e=\cfrac{1}{2}$$

using this common ratio in Eq[1], we have ..

$$a=-400$$

So, first term is $a=-400 \space \&$ common ratio is $e=\cfrac{1}{2}$ .