Question

The first and eighth terms of a g.P. Are 3 and 2 respectively, then find the value of 'p' provided it's the product of first eight terms of the corresponding g.P

Answer 1

Answer:  The answer is 1944.

Step-by-step explanation: Let 'a' and 'r' be the first term and common ratio of the geometric progression (G.P.). The first term and eighth terms are 3 and 2 respectively.

So, we have

$a=3~~~\textup{and}~~~ar^{8-1}=2~~\Rightarrow ar^7=2.$

Dividing the second equation by first, we have

$r^7=\dfrac{2}{3}.$

Therefore, the value of 'p' is given by

$p=a\times ar\times ar^2\times ar^3\times ar^4\times ar^5\times ar^6\times ar^7\\\\\Rightarrow p=a^8r^{1+2+3+4+5+6+7}\\\\\Rightarrow p=a^8r^{21}\\\\\Rightarrow p=3^8(\dfrac{2}{3})^3\\\\\Rightarrow p=3^52^3=1944.$

Thus, the value of p is 1944.