Answer :

Suppose the 1st term is a and the common ratio is r.


we can say that GP looks like: a ,ar ,ar2 ,…


According to question:


a + ar = 5 …equation 1


Also, a1 = 3(a2+a3+a4+…∞) {you can take any other combination}


a = 3(ar+ar2+ar3 + …∞)


1 = 3(r + r2 + r3 +…∞)


We observe that above progression possess a common ratio. So it is a geometric progression.


Common ratio = r and first term (a) = r


Sum of infinite GP = ,where a is the first term and k is the common ratio.


Note: We can only use the above formula if |k|<1


we can use the formula for the sum of infinite GP.


Therefore



1-r = 3r


r =


From equation 1:


a+ar = a(1+r) = 5.


So,



a = 4


GP is (4 , 1 , 1/4 , 1/16 , ….)


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