Question

The 4th term of a geometric progression is 2/3 and the seventh term is 16/81 . find the geometric seires

Answer 1

Answer:

9/4, 3/2, 1, 2/3, ....

Step-by-step explanation:

$a_{n}=ar^{n-1}\\\frac{a_{7}}{a_{4}}=\frac{ar^6}{ar^3}\\\frac{\frac{16}{81}}{\frac{2}{3}}=r^3\\\frac{8}{27}=r^3\\r=\frac{2}{3}$

$\frac{2}{3}=ar^3=a\frac{8}{27}\\=>a=\frac{9}{4}$

Therefore the G.P is 9/4, 3/2, 1, 2/3, ....