The common ratio of a Geometric Progression is 2 . If the 5 th term is greater than the ist term by 45 . find the 5 th term
A. 3 B. 8 C. 45 D. 48
Correct Answer: D
Explanation
Given: common ratio \(r=2\) 5th term \(U_{5}=a r^{n-1}=a r^{5-1}=a r^{4}\) since \(U_{5}>u_{i}\) (i.e. a) by 45 . then. \begin{aligned} U_{5}-a &=45 \\ \Rightarrow a n^{4}-a &=45 \\ a\left(r^{4}-1\right) &=45 \\ a &=\frac{45}{r^{4}-1} \\ \text { put } r &=2 \\ a &=\frac{45}{2^{4}-1}=\frac{45}{16-1} \\ a &=\frac{45}{15}=3 \\ U &=a a^{4}=3(2)^{4} \end{aligned} \(=3(16)=48\)