Question

Find the first term and fourth term of the given sequence-

$1400,700,350....$

Answer 1

Given:First term$=a=1400$

Second term$=700$

Common ratio$=\frac{700}{1400}=\frac{1}{2}$

$=\frac{350}{700}=\frac{1}{2}$

$\therefore$ Common ratio $r=\frac{1}{2}$

Hence the given sequence is in G.P

$n^{th}$ term$=t_n=a{r}^{n-1}$

Fourth term$=t_4=1400\times {\left(\frac{1}{2}\right)}^{4-1}$

$=1400\times {\left(\frac{1}{2}\right)}^3$

$=1400\times \frac{1}{8}$

$=175$

Hence, the first term is $1400$ and the fourth term is $175$