Question

The sum of an infinite g. P. Is 23 and the sum of squares of infinite terms is 69, then find first term

Answer 1

Answer:

a = 69/13

Step-by-step explanation:

Let say infinit GP

a , ar  , ar²  , ar³ ....

Then Sum = a/(1 - r)  =  23     eq1

Square of GP Terms

a²  a²r²   a²r⁴   a²r⁶  ....

Sum = a²/(1 - r²)  = 69     eq2

Eq1² /Eq2

=> (1 -r²)/(1 - r)² =  23/3

=> (1 + r)/(1 -r) = 23/3

=> 3 + 3r = 23 - 23r

=> 26r = 20

=> r = 10/13

a/(1 - 10/13) = 23

=> a = 69/13

First Term = 69/13