Geometric Progression - For geometric progression multiplication of 5 terms is 1 and 5 th term is 81 times then the 1 th term. calculator

SolutionExample

This is demo example. Please click on Find button and solution will be displayed in Solution tab (step by step)

Geometric Progression

7. For geometric progression multiplication of 5 terms is 1 and 5 th term is 81 times then the 1 th term.

Let the terms are

(ar2),(ar),a,(a×r),(a×r2) $(a / r^2) , (a / r) , a , (a × r) , (a × r^2)$

Multiplication :

(ar2)⋅(ar)⋅a⋅(a×r)⋅(a×r2)=1 $(a / r^2) * (a / r) * a * (a × r) * (a × r^2) = 1$

⇒a5=1 $=> a^5 = 1$

⇒a=1 $=> a = 1$

Now

5th $5^(th)$ term is

81 $81$ times than the

1st $1^(st)$ term

⇒(a×r2)=81(ar2) $=> (a × r^2) = 81 (a / r^2)$

⇒r4=81 $=> r^4 = 81$

⇒r=3 $=> r = 3$

Now,

a=1 $a = 1$ and

r=3⇒(132),(13),1,(1×3),(1×32)⇒0.1111,0.3333,1,3,9 $r = 3 => (1 / 3^2) , (1 / 3) , 1 , (1 × 3) , (1 × 3^2) => 0.1111 , 0.3333 , 1 , 3 , 9$