Question

the sum of the terms of an Infinity decreasing geometric progression is 3 and the sum of the cubes of is terms is 108/13 write the progression ​

Answer 1

Answer:

ANSWER

Let the GP be a,ar,ar2,... where 0<r<1.

Then a+ar+ar2+...=3 and a2+a2r2+a2r4+...=29

⇒1−ra=3 and 1−r2a2=29

We have 1−ra=3⇒a=3(1−r)

∴1−r29(1−r)2=29

⇒1+r1−r=21

⇒r=31

Putting r=